Afterwards, the pair fell into conversation and the Arsenal chief revealed to Clark that he would not want to work in the lower leagues as defeats are so frequent.
The former England international understood fully what Wenger meant, saying later about the chat that took place after a League Manager Association-organised event at the Emirates Stadium: "Everything he said has stuck in my mind. I am not a bad loser in that I always congratulate the opposition and shake hands, but I hate losing. It hurts."
If Clark is feeling the pain of defeat this morning following Town's FA Cup exit, surely it will be tempered hugely by the pride felt at how his side performed in north London.
Huddersfield came within four minutes of earning what would, on the balance of play and number of chances created, have been a fully-deserved replay.
After weathering an Andrei Arshavin-inspired early bout of pressure from the Gunners, Town grew in confidence to such an extent that for long periods of the second half it was the League One club that looked the more likely side to snatch a winner.
By then, Arsenal had not only been reduced to 10 men following the dismissal of Sebastien Squillaci but also seen their half-time lead cancelled out by Alan Lee's first goal in Huddersfield colours.
Unfortunately for Town and their vocal travelling army of fans, justice was not done with it being Arsenal who prevailed courtesy of Cesc Fabregas firing an 86th- minute winner from the penalty spot.
Nevertheless, as the Huddersfield squad returned north yesterday, it was with their heads held high after rattling a team who just a few days earlier had booked their place in the League Cup final.
Clark said: "I am very, very proud of my players. They all worked extremely hard and it was disappointing not to get something from the game.
"All my players can be proud of their individual efforts as they were excellent. We passed the ball well and created chances, while restricting them to just a few opportunities.
"We have to take encouragement from that performance. Our ultimate goal is to get promoted so what we have to do now is go about our job like we did against Arsenal.
"If we play to that level then we will get the wins we want."
Clark's sense of pride was understandable with even Wenger admitting afterwards that Arsenal's record of never having lost to lower-league opposition in the FA Cup under his charge had been "under threat at 1-1".
The Frenchman's concern was understandable considering the way Town had battled back from being penned back in their own half in the early stages.
In that opening quarter, Arshavin blazed over and then struck a post while Nicklas Bendtner was guilty of wasting a couple of excellent openings.
The second of those saw the Dane fail miserably to control a beautifully flighted pass from Samir Nasri on 21 minutes but he made amends just moments later.
This time it was Marouane Chamakh who found Bendtner, who controlled and drilled a shot that took a deflection off the chest of the unfortunate Peter Clarke before nestling in the corner of the net.
If the 59,375 crowd and the viewers watching at home on ESPN thought this would merely be the prelude to Arsenal coasting into the fifth round they were very much mistaken.
First, a neat one-two with Jack Hunt allowed Anthony Pilkington to race clear and drill a ball that Lee should have done better than stab wide.
Pilkington then wasted two chances, dragging a shot past the post after a mistake by Denilson and then heading wide from close range when picked out superbly by Joey Gudjonsson.
Huddersfield's growing confidence was underlined four minutes before the break by a stunning 60-yard dash by Jack Hunt that was only ended by a crude foul from Squillaci that brought the French international a deserved red card.
The upshot was Town sensing a shock really could be in the offing, as proved by the opening 20 minutes of the second half being a near-constant procession towards the home goal.
First, Manuel Almunia denied Gudjonsson and then Arshavin produced a goal-saving tackle on the Icelandic midfielder inside the six-yard box.
Jamie McCombe also headed wide before Almunia produced the save of the game to claw away a Lee header that had seemed destined for the net.
To a striker who in 25 previous appearances for Huddersfield had failed to find the net, a save of such high standard could have been taken as proof that such a barren run was not going to end at the Emirates.
Lee, though, refused to be denied and broke his duck just three minutes later when rising high above the Arsenal defence to power Pilkington's inviting cross beyond Almunia. Suddenly, the unthinkable seemed possible as Town went in search of a winner that would have made headlines across the globe.
There was, however, to be no happy ending for Town with sloppy defending four minutes from time leading to possession being squandered on the edge of the penalty area.
The ball was quickly worked towards Bendtner, who took a tumble under pressure from McCombe and referee Mark Clattenberg pointed to the spot.
Town manager Clark had few complaints afterwards, saying: "From where I was in the dugout, it looked like a penalty. A couple of the lads, including the goalkeeper, said it wasn't but what matters is it was given."
Fabregas, who had been brought on by a visibly worried Wenger 16 minutes earlier, coolly stepped forward to send Ian Bennett the wrong way and end Town's hopes of an upset. Nevertheless, Wenger was full of praise for the Yorkshire side. He said: "It was tough, tough, tough. Huddersfield are a good team and they showed that.
"Our record (of never having lost an FA Cup tie to lower-league opposition) was under threat at 1-1 because they were creating chances. We looked tired but, in the end, we had the quality to make the difference."
Hero: Alan Lee
It just had to be. After 25 appearances and five months of frustration, Lee picked the optimum time to break his scoring duck. The hope for Lee Clark now is that the striker can now use his first goal in Town colours to inspire a scoring run that will make light of top scorer Jordan Rhodes being out for up to two months.
Villain: Cesc Fabregas
One of European football's leading talents but could still do with showing a bit more class as a person than he did yesterday. Taking the ball into the corner after scoring what turned out to be the winner was cynical in the extreme, as was his attempts to slow down play late on by holding on to the ball when Town had a throw-in – an action that brought a deserved yellow card. Also tried to get Jamie McCombe sent off in the wake of the penalty decision by waving an imaginary card at the referee.
85th minute: When the ball was rolled into the six-yard box and Nicklas Bendtner had got goalside of Jamie McCombe, it was clear Town were in real trouble. So it proved with a tug on the Danish striker proving enough to persuade Mark Clattenberg to point to the spot, allowing Fabregas to win the game.
Mark Clattenberg: Showed sensible handling of the tie and allowed play to continue whenever possible, something that added to the entertainment value. Got the big calls right with Sebastien Squillaci deserving to go and McCombe being guilty of a tug on Bendtner. The only questionable decision was whether the Town defender deserved a red card for denying a clear goalscoring opportunity.
A proud day for Huddersfield Town, who Arsene Wenger admitted afterwards had come close to ending his proud record of never having lost to lower-league opposition in the FA Cup. To come within four minutes of bringing Arsenal back to the Galpharm Stadium is a huge testament to the efforts of the visitors and it is hoped Town can now take this level of performance into the League One promotion race.
Quote of the day
Lee, I need a right winger – how are you fixed?
– Arsene Wenger jokes with Lee Dixon in the post-match press conference about the current spate of injuries in N5.
Huddersfield Town v Carlisle United; Tomorrow, 7.45pm; League One.
Fabregas relief at late winner
Arsenal captain Cesc Fabregas was delighted to avoid a replay after his late penalty saw the Gunners past Huddersfield and into the FA Cup fifth round.
Fabregas ensured a 2-1 triumph by netting from the spot after Nicklas Bendtner went down under Jamie McCombe's challenge.
The climax was similar to the third-round draw with Leeds, but Fabregas said: "Today we won and we are happy we don't have to play an extra game.
"We are in Europe and playing the best team in Europe, so we don't need an extra game."