The substitute scored the only goal to settle the contest 1-0 after collecting a pass from fellow replacement Drey Wright as the Gills suffered a losing start on their return to League One.
U's boss Dunne, who started his playing career at Gillingham, said: "It's a difficult place to come and we knew that it would be a hard afternoon.
"Gillingham is a good club with good fans but I thought we did a job and we were tremendous - everyone played to their limit.
"We had to defend a lot from throws and set plays into the box but I thought that we deserved our win and I'm very pleased with how we went about our business.
"We analysed every goal they scored last year and long throws and corners were defended well against them, in a different division.
"We used our substitutes wisely and we had a plan and stuck to it.
"We had to be resilient at times and you have to earn the right to play in any game that you play.
"We had to scrap at times but the goal looked like it was coming and we managed to get in behind their back four.
"It's a good win for us but it's only the first game and we'll be back in on Sunday morning, getting ready for the Peterborough United cup tie on Tuesday night.
"We're focusing on one game at a time and we'll treat every game like a cup final this season and see where that takes us."