Chances were at a minimum during the first half, but Brentford made all the early running after the break and Adam Lockwood produced a timely interception to deny Leon Legge a chance at point-blank range, while Clayton Donaldson wasted a great chance in injury time.
"It was a fair result and a good result," said Rosler. "The first game is always difficult.
"We got the first clean-sheet of the season. We came here to get a result and we got one point. Overall, we are one point up from last season.
"In the first half, we invited too much pressure. Our midfield stood a little too deep and we weren't brave enough to attack more. We got that right in the second half.
"(Shaleum) Logan started to bomb down the right-hand side. We knew there would be so much room to attack and in the second half, we used this very well. I was very happy with that but then Bury started to gain some momentum. In the end, it is a fair result."
