The League Two managed to keep the game level for the first-half at Old Trafford.
But United returned from the dressing room reinvigorated and blitzed Colchester with three goals in ten minutes.
Speaking after the game, midfielder Nemanja Matic said: "As you saw it was a hard game for us. I think in the first half we played much better but in the second half we scored three goals, which is strange.
"In the first half we were in complete control in the second half they had one or two counter attacks which were dangerous but then we could also take advantage of the space.
"I'm more happy with the first half but in football you never know. I'm happy we are through and hope we can reach another final to win a trophy."