Brett Pitman's well-taken strike helped the Cherries boost their automatic promotion hopes.
Howe said: "With five games to go, we've put ourselves into a very strong position. We're aiming to win all of those games and we might need to because other teams have got games in hand.
"But we're a very modest group and we've come from a long way behind to get to where we are now. We've got everybody fit now and you just have to listen to the music coming from the changing room to hear what it means to us. I thought that the lads were excellent.
"We had to hang in a bit towards the end but I don't think that our goalkeeper has had a shot to save.
"I actually thought that it was one of our best performances because we dominated possession on a difficult surface and created numerous chances.
"We probably weren't clinical enough with them but that's probably the only criticism of the day."
Bournemouth's Lewis Grabban was denied by Colchester goalkeeper Sam Walker before Pitman fired the visitors ahead after 19 minutes with a first-time shot at the near post from Matt Ritchie's low cross.
Marc Pugh's header struck the post and Grabban wasted a gilt-edged chance in first-half stoppage-time as the visitors went in search of a second goal.
Harry Arter forced Walker into action three times in the second half as Bournemouth secured a vital win.