David Carney's first goal for United in the 42nd minute was enough to separate the two sides.
It was Bolton's first home defeat under Megson but he said: "I do not regret making those changes.
"We picked a team with an eye on what has gone on with most of the players having a lot of games in a short space of time.
"A lot of clubs have done this today. The disappointment is that a number of players did not take the chance given to them.
"They are highly-paid Premier League squad members, who did not rise to the challenge.
"There was an assumption from one two there will be another chance and you can't do that."