The Owls bounced back from a 3-0 defeat at Hull on Saturday to edge out their Sky Bet League One hosts thanks to Atdhe Nuhiu’s goal, moments after half-time of this third-round replay.
Agnew said: “I’m really pleased with the players, it was a very tricky tie and I thought we stood up to it well.
“Luton did push us back after we got the goal, and (goalkeeper) Cameron (Dawson) made one or two really good saves and they hit the post, but so did we first half through (Steven) Fletcher.
“From a spectator point of view, it was a terrific FA Cup tie.
“I just think it was a spirited performance, we showed passion, energy, effort and determination, and that’s what asked after the weekend.
“We just wanted a reaction from all the players and that’s what we got.
“Now we have a terrific cup-tie to look forward to at Chelsea and we’re looking forward to that.”
The visitors went closest first with Adam Reach off target before George Boyd fired over the top.
Luton saw Jack Stacey’s effort easily held out by Dawson, while James Collins dragged an effort wide.
The Owls almost had the lead after 36 minutes as Barry Bannan’s volley was flicked on to the post by Steven Fletcher.
Elliot Lee put a brilliant chance over the crossbar, with Dawson saving well from James Justin’s long-range shot.
The visitors led at the start of the second period after Nuhiu’s effort deflected past home stopper James Shea from close range.
Luton should have levelled as Justin picked out Luke Berry, who was denied by the legs of Dawson.
Hatters interim manager Mick Harford felt his side deserved more from the evening, after visiting goalkeeper Dawson made a string of fine saves.
He said: “I thought they were magnificent, against a Championship team, we went toe-to-toe for 90 minutes.
“They had a little spell in both halves where they’ve dominated possession a little bit, but never really hurt us.
“I think chance-wise, shots-wise we dominated them and are very, very unfortunate to not come away with some kind of result.
“I’m very proud of the players, the way they go about things, the way they’ve trained, the way they’ve worked hard, the way they played.
“They’ve got a great attitude to winning for this football club and I’m really happy with the performance.”