Two goals in four second-half minutes from Anthony Wordsworth and Freddie Sears gave the U's victory and ended their run of three straight defeats.
Dunne said: "I thought it was well-deserved and we were the better team. We knew it was important coming off the back of those three games that we spoke about quite publically.
"I put my trust in my team selection and they came through. We trained really well in the lead-up to the match and I thought that we deserved to win.
"Bury pushed forward in the second half to give us a bit of space to work in. I thought that we were patient in the first half and dominated the ball. We moved it well and patiently and had opportunities.
"The patience paid off in the second half and we got two great goals again. We like to work our goals and we have clever players, who just need to believe a bit more in what we're capable of."