A goalless draw appeared on the cards for much of the Elland Road contest but Kyle Bartley nodded in Stuart Dallas' cross two minutes from time to give Leeds a hard-earned 1-0 victory.
It was the 13th time Leeds had scored after the 82nd minute this season and Monk has urged his players to continue to fight until the end.
"We've won seven of our last nine home games and that's great," said the Leeds head coach. "But it was obvious we weren't at our best today. I thought we looked tired, especially in the first 60 minutes.
"The one thing this team has - we try instil it in them - is that belief to fight every second they're on the pitch.
"The sense was that it was going to be one of those days but it was a great header from Barts and I think the roof came off the place when that goal went in.
"It's great to see that mentality, fight and spirit from the players to keep going right to the end.
"It's something we've been doing a lot and building a lot on, and that's what you need to do.
"In close games like this where we've not quite been on our level we've found a way to win.
"All in all in this period we've just had, the players have done very well and deserve a lot of credit."
Leeds will aim to consolidate their play-off position when they travel to Preston on Boxing Day and Monk revealed they could be boosted by the return of key duo Pablo Hernandez and Chris Wood.
"Pablo only trained for two days and wasn't quite right so this game came too soon for him," said Monk. "He'll have a good week's training now and will be back in contention for next weekend.
"We're hoping Chris will be involved in the latter stages of next week and hopefully he'll be available for the Preston game."