Club legend Ryan Giggs has taken charge on an interim basis until the end of the season, but Monk believes Moyes should have been afforded more time to mould the team.
"It does take time. Going into that club as he did, following someone so successful, is always going to be hard," Monk said.
"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."
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