Jermaine Easter's first-half penalty and Mark Carrington's ice-cool 55th-minute clincher knocked the managerless Us off top spot, before Scott Vernon pulled a goal back late on.
Paul Lambert left Colchester for Norwich this week and Dunne is hoping a replacement is found soon, saying: "The players were magnificent but this defeat will probably accelerate the process of a new manager being chosen.
"It's been a tough week - we've had the manager walking out on Tuesday, our captain Dean Hammond being sold, Johnnie Jackson leaving and a transfer request being handed in by David Perkins on Friday night.
"I'm doing the job to the best of my ability but the candidates they are speaking to are of a very high standard.
"Lee Beevers also had to come off with a dislocated shoulder so whoever the prospective new manager might be will have to have some players lined up to come in. We need to look at the squad size, we need one or two in urgently."