Leading thanks to Steven Fletcher's 11th goal of the campaign in the first half - just reward for a dominant opening 45 minutes - Wednesday repelled the hosts on the restart and looked set for their third successive league win for the first time since September 2018.
But Derby, who were much improved on the restart after a dismal first period, restored parity from the spot after Moses Odubajo was penalised for a challenge in the box on substitute Jack Marriott.
The former Hull City and Brentford player then saw his evening take another turn for the worse after he received his marching orders late on for a second bookable offence.
The night also saw Sam Hutchinson pick up his tenth yellow card of the campaign, incurring a two-match ban which will rule him out of the forthcoming games against Nottingham Forest and Bristol City.
Monk, who revealed that Fletcher came off in the second half with a hamstring niggle, said: "He (Odubajo) gives the referee a decision and the referee has made that decision and we have to live with that.
"Mo is in front of the player. It could be a foul on Mo or the other player. It was a 50-50 one, which went against us on this occasion and we have to take it."
On his side's performance, on an occasion when a 2-0 victory would have seen play-off chasing Wednesday move up to third place, Monk added: "We had a lot of quality in that first thirty minutes and were creating a lot of situations and we were very unlucky not to get another goal.
"But after that, physically as well, we have had a lot of games and looked a little bit leggy towards the end. Understandably.
"It was a very scrappy game and not enjoyable to watch after the first 35 minutes. Both teams found it difficult really and were feeding off scraps and I suppose from an away perspective - even though we were in that winning position towards the end - we will have to look at that as a point gained as we had ten men at the end."
On the performance of Jordan Rhodes, handed his first start in the league for the club since April 2018, the Owls chief continued: "He did well. In that first 35 minutes, we were right on the front foot and he looked very good and really sharp and got in really good situations.
"But after that, it was a really scrappy game. We could have won it, but also could have lost it with the situation of going down to ten men."