The Championship side made eight changes ahead of Monday's tie, but despite falling behind to their League Two opponents, they rallied round to secure a 2-1 win at the Abbey Stadium.
Monk said after the game: "Cambridge made it very tough for us as we knew they would... we were able to move the game up the pitch in the second half and got the goals at good times.
"I trust all my players - there's no point in having a squad if you are not going to use them and it will stand them in good stead.
"I love the FA Cup, I've grown up with it and it means a lot to me. All I know is that we use our squad, we respected it and you could see that from how committed we were."
AFC Wimbledon or Sutton United will host Leeds in the fourth round of the competition.