Monk's men head to Kenilworth Road on Wednesday evening chasing a first Championship victory since January 11.
They face a Hatters side that are in danger of being cut adrift at the bottom after losing six of their last seven league matches.
Monk, whose team were held to a draw by lowly Barnsley last weekend, said: "It will be a similar game to Barnsley in the sense that it will be a battle.
"We know they are scrapping for their lives and we are going to have to match that. It is a quick turnaround.
"We competed against Barnsley but we need to show more composure and that's what we need to improve for Wednesday.
"With the ball, they are good players. They just need to trust themselves and make better decisions with the ball at the right times."
Despite overseeing only one Championship win since Christmas, Monk is convinced it is only a matter of time before they turn things around.
"WIns give you belief," he said. "You can see the fight and attitude is there.
"We are trying to do the right things.
"If we can get that win, you can often turn that corner and put you on certain types of run.
"But no one is going to give it to us. It is even harder when you are playing against these teams (at the bottom) because we are the stage of the season where they are fighting for their lives.
"We need to fight for our lives. We have to keep pushing the players to show that confidence and belief in themselves."
All eyes will be on Monk's team selection as the Owls target a league double. Forwards Fernando Forestieri, Alessio Da Cruz, Josh Windass and Connor Wickham could keep their places, although wingers Jacob Murphy and Kadeem harris are pushing for recalls.
But Moses Odubajo (hamstring), Adam Reach (toe), Massimo Luongo (groin) and Morgan Fox (ankle) remain major injury doubts.