Monk's side moved above their rivals and up to sixth in the table after two second-half goals from Steven Fletcher secured all three points at Hillsborough.
The Owls' top scorer took his tally to 10 for the season as Wednesday came back from a goal down, with Bryan Mbeumo opening the scoring for Brentford in the first half.
Monk said: "I think that the players deserve huge credit for turning that game around from the position we were in to come back in that second half and win it.
"We know we were way below the levels that we expect in that first half, but speaking about that expectation at half-time and to come back against a hugely impressive side, the team deserve huge credit for that.
"When I came into the club, maybe there was a criticism that when they fall short of that level, they weren't able to come back from that type of situation.
"That was something I spoke about that we needed to change, and you can see with the determination that these players have got, they want to do that as well."
Monk was also pleased for match-winner Fletcher, saying: "It's great when your strikers score goals, and we want to keep him in that form.
"His overall performance, like the rest of the team, epitomised that attitude that we want and we played with intensity in that second half so that was really pleasing to see."
Brentford manager Thomas Frank bemoaned his side's lack of composure and quality in the second half.
His team took the lead through Mbeumo in the 29th minute and could have equalised late on as Said Benrahma broke away from his defender, but his curled effort went agonisingly wide as Wednesday held on.
Frank said: "This is Championship football, so anything can happen. We played a really good first half away from home in a lot of aspects.
"We didn't give any chances away, we played a good high line, we closed most of the crosses down and we created a lot of opportunities to go 1-0 up.
"Maybe we should have taken one of those chances to make it 2-0 because we know anything can happen in this league.
"The most disappointing thing was that we lacked that 'coolness' in terms of sometimes just keeping the ball or sometimes go for the kill.
"We lacked quality and decision-making and that extra good touch or pass to make it two-nil.
"Then after the equaliser from a strange penalty, we needed to stay in the game. We were absolutely sleeping from that quick throw-in.
"We knew that they wanted to put crosses in the box, we knew that Fletcher is a good striker so that goal is a very disappointing moment because I think 1-1 would still have been a good result here.
"In general, when you play so well in the first half you want at least a point, but football matches are 90 minutes and we need to do well enough over those 90 minutes but we didn't do that today."