The Bees were denied the chance of an injury-time penalty when striker Clayton Donaldson was bundled over by Bournemouth midfielder Eunan O'Kane.
Ref Robinson waved play on, sparking furious scenes on the touchline as Rosler remonstrated with the fourth official.
Rosler said: "There was a lot of noise coming from their dug out to the fourth official throughout the game and as a management team we felt we had to stand up for our team.
"Their player had no intention of going for the ball. He jumped at Clayton and I thought it was a clear penalty."
Rosler felt Robinson's display tested his young side's mental strength with what he saw as a string of inconsistent decisions.
"There were a lot of 50-50 decisions going their way in the second, which simply underlines the huge mental strength of my players for digging even deeper to make sure they didn't get beaten," Rosler said.
The battle of npower League One's two form sides rarely looked like ending in anything other than stalemate as they cancelled each other out.
The Bees, unbeaten in 11 matches, and the Cherries, without a defeat in 15, created few chances in a game of cat and mouse.
Rosler added: "Bournemouth financially are a big side, but our team has been put together on a fraction of what theirs cost and is as good," he said.
- Sports & Recreation
- Clayton Donaldson