The Bees twice led European champions and Cup holders Chelsea thanks to goals from Marcello Trotta and Harry Forrester, but Oscar grabbed the Blues' first equaliser and Fernando Torres spared their blushes seven minutes from time.
It means the League One high-flyers get a money-spinning trip to Stamford Bridge and another shot at dumping out their illustrious west London neighbours.
"Overall, my players did fantastically. They earned the right to play at Stamford Bridge," said Rosler.
"It will be a great day for our supporters again, for our players and, financially, it will help enormously.
"Also, congratulations to my players for what they did individually and collectively. That was top-drawer."