The Whites had to fight back to avoid a third round upset after Cambridge took a first-half lead in Monday night's clash on the battered Cambs Glass Stadium turf.
Leeds were pegged back in the early stages but were more assured after the break and they made the momentum swing count with two headed goals in the second-half.
“We knew it was going to be tough and thankfully we came through it,” said the Whites boss, speaking on the Alan Brazil Sports Breakfast.
“It was a terrific cup tie - credit to Cambridge because they really came out of the blocks and they put us under pressure.
“But we stayed calm, we were doing all the right things but were just playing it around too deep and inviting them on to us.
“I told the lads at half-time to keep going and just make sure to do it further up the pitch. Once we put them on the back foot I felt like we had control, thankfully we took our chances and we’re into the next round.
“It was a great comeback, a great performance, and it stands us in good stead for the next round and the rest of the season.”
Monk has overseen a steady turnaround not just in results, but also the shape and attitude of the team since his appointment in June.
After a run of six games unbeaten in all competitions, Leeds currently sit in fifth place in an extremely competitive top end of the Championship table and are just seven points adrift of the automatic promotion places.
Getting back to the top flight is one of the club’s top priorities, and while Monk shied away from bigging up their promotion hopes, he did hail his side’s hunger to learn, improve and – best of all – win.
“I’ve got a great group here,” the 37-year-old added.
“They’re very young and not the most experienced lads, but what they have is tremendous desire and heart to try and improve, to try and win games.
“We have a strong mentality and a good spirit and we obviously work very hard on the training ground. Of course once you get on a roll you get the taste for it and you want to try and keep it going.
“They’re all listening and they’ve got a desire to learn, so it’s a great group to work with as manager.
“I don’t think we’ve reached anywhere near our full potential yet, I think we’re still very early in that process, but we’re making good strides along the way.”
Read more at http://talksport.com/football/listen-fa-cup-comeback-stands-leeds-united-good-stead-rest-season-garry-monk-talksport#sHa3yCAUKWdQJ3JD.99