Despite offering the former Everton boss a six-year contract, 15 defeats in all competitions as well as the failure to qualify for next season's Champions League, spelled the end for Moyes.
"It does take time," Monk told reporters. "Going into that club as he did, following someone so successful, is always going to be hard.
"For any manager, you need time, but nowadays, as we see time and time again in this job, you simply just don't get the time. It is results-driven, especially for a club like Man United that is expected to be winning a lot of trophies every single season."
With regards to his own future, Monk expects to hold talks with the Swansea board at the end of the season.