Goals from second-half substitutes Yoann Arquin and Romello Nangel sealed the three points for mid-table County after the first half had finished level at 1-1.
Jabo Ibehre had earlier levelled for the U's after Jeff Hughes had put the hosts in front in an extended first half which was marred by a delay of over 10 minutes following an injury to Colchester's David Wright in a clash with Joss Labadie.
First thoughts after the full-time whistle, therefore, were regarding the health of the full-back.
Dunne said: "David is at the hospital at the moment. He got clean knocked out and we were worried about his neck as well so all the precautions were taken to make sure he was removed from the ground in a safe manner and I have to credit everybody for that.
"I haven't seen him as they took him straight to the hospital for a scan but we know he's okay and we will go and pick him up and take him home."
On the pitch Dunne felt it was a missed opportunity and now feels his side need to win all their remaining games to avoid the drop.
He added: "It could come down to goal difference and you can't be conceding two's and three's so I'm particularly frustrated with their third goal.
"We've cleared the air in the dressing room and now we have to go and win all our games. That's the end of it. We've got to win all our games to avoid the drop."
- Sports & Recreation