The Sky Blues were already 1-0 up through Franck Moussa's strike when William Edjenguele's header was controversially allowed to stand, despite the assistant referee initially flagging Gary McSheffrey offside.
Tom Eastman gave Colchester hope with 19 minutes to go, but in-form David McGoldrick wrapped up the points for Coventry late on.
Robins said: "We played really well and I thought we were outstanding. We passed the ball really well and it was an outstanding team performance.
"The first goal we scored as a team goal was excellent. The passing, the delivery and the execution of the goal was first class."
Robins, whose side have risen to 15th, nine points off the play-offs, added: "You have to take each game on its merits, but we've played well in our last two away games. I'm delighted with that and we'll be looking to take that form into the next game.
"We have two home games now and we'll look forward to those, because we've got confidence."