Fans chanted that the German would be sacked in the morning after Magnus Ukuonghae had given the visitors the lead just after the break and when Rosler substituted Adam Forshaw with 20 minutes remaining.
"I'm very disappointed in a small section of the fans who chanted that," Rosler said.
"I'm always happy to give our fans a lot of time, so when they sing that I think it's out of order.
"This club is not an open book. Only I know that Adam Forshaw has been sick and that Marcello Trotta has looked excellent in training, but the fans do not."
The supporters' jeers turned to cheers as the goals turned the game on its head.
Rosler added: "As soon as we equalised the confidence came back and it was like the old days.
"We never gave up, every player dug in and never gave up.
"Now we have to get that consistency and go on from here, but it did show how thin the line is between success and defeat.
"Overall though, I thought we played very well."
Ukuonghae gave the visitors the lead just after the break, rising unmarked to power home Luke Garbutt's corner.
But the Bees hit back in the 76th minute when Trotta slotted home Clayton Donaldson's low near-post cross.
Chelsea loanee George Saville put the home side ahead with 10 minutes remaining, firing home a curling drive from the edge of the area.
And the comeback was complete with minutes to go when on-loan Cardiff winger Kadeem Harris headed his debut league goal from Sam Saunders' precision cross.
Brentford might have gone in ahead at the break, but Trotta fired wide from three yards when it looked easier to score.
- Sports & Recreation
- Marcello Trotta
- Kadeem Harris
- Adam Forshaw