Late goals from debutant Jabo Ibehre and substitute Freddie Sears gave the U's their first win since November and helped them climb out of the relegation zone.
Dunne said: "I thought it was a well-deserved win, especially on our second half performance.
"We had to be very competitive, in terms of the gameplan.
"It wasn't a great game, in terms of style or football.
"But when you are where we are you have to dig in and I thought it was a really good performance.
"It's been a long time coming and the fans showed great patience. They've been magnificent and the staff have been very supportive of me, along with the chairman.
"I'm really pleased for everybody - players, staff, fans and the chairman.
"When we spoke at half-time we said that we were in the game and we felt we could go on and win it and that's what we did.
"We played like an away team in the second half, but David (Wright) sat in front of our back four and did exceptionally well and had a great debut."