Brett Pitman's well-taken strike helped the Cherries boost their automatic promotion hopes and left Colchester's cushion above the bottom four to just three points.
Dunne said: "We need a lot more if we're going to survive. It was a frustrating game all round and we can do a lot better.
"A defeat is a defeat at this stage of the season, it doesn't matter whether it's narrow or four, five or six.
"We've come away with nothing after making things difficult for ourselves. We had a good crowd in but we didn't give them much to cheer about. We didn't want a two-week break to be an excuse and it's not.
"We started the game really well and we needed a goal at that stage. We had a couple of half chances but then we dropped a bit deep and stand off them.
"The goal was coming and once they got it, to be honest they totally controlled it in the first half. They should have scored again and we huffed and puffed but it wasn't enough."
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.