The Bees led 2-1 until referee Paul Tierney changed the game when he showed on-loan Everton defender Jake Bidwell a second yellow for an innocuous challenge.
Brentford, who face FA Cup holders Chelsea on Sunday, had a let-off when Simon Moore saved David Mooney's penalty but eventually let the lead slip with four minutes remaining when Lee Cook lashed home an unstoppable drive from the edge of the box.
Goals either side of the break from Paul Hayes and Clayton Donaldson had given them the advantage after ex-Bee Martin Rowlands fired home a 30-yard free-kick eight minutes in.
Bidwell will miss the clash with the European champions, but Rosler was quick to praise his contribution.
"Jake has been fantastic for us this season but as soon as I saw the ref blow and look at him I knew what he was going to do," said Rosler.
The German was also disappointed with the official's failure to spot a clear Mathieu Baudry handball in the box and tried in vain to show him the footage.
He said: "Once we were down to 10 men the course of the game changed, but we fought like heroes and didn't want to get beaten. In the end we didn't get what we wanted but my players were fantastic.
"We didn't get what we wanted and we are gutted about that but we had to fight against other elements, and I know we can play better than that."
- Sports & Recreation