Moore allowed Dean Bowditch's long-range shot to squirm underneath him to gift the Dons a 14th-minute lead before Stephen Gleeson netted late on to seal the Dons' second successive win.
But Rosler refused to blame Moore after his side's three-match winning run came to an end - and instead pointed the finger at some of his outfield players.
He said: "We win together and we lose together but I'll be responsible for the result. I thought we were more than in control, the first goal is always important.
"Simon Moore has been terrific for us all season, he's a young player so he's allowed to make mistakes - hopefully not too many. I will not blame him at all.
"I was disappointed with one or two players but the majority of the players did very well."
Bowditch put the Dons ahead against the run of play when his speculative 25-yard shot slipped past the grasp of Moore and into the corner of the net.
Trotta and substitute Bradley Wright-Phillips both missed golden opportunities to equalise for Brentford before Gleeson sealed it for the Dons five minutes from the end when he lashed in Darren Potter's cutback.
Dons boss Karl Robinson said: "All I care about is the result. It wasn't pretty, it wasn't us at our best but I don't think you've seen Brentford at their best either.
"And for me to have seven players out, that's not a bad performance against Brentford. I thought the way the boys put their bodies on the line was excellent. We still live in hope, we will keep going to the end."
- Sports & Recreation
- Stephen Gleeson