The five-game tournament had taken it's toll on Rovers as they played their final game of the Spartak Cup with only ten men due to injuries sustained to Scott Wharton, Stuart Callaway, Mark Edgar, Lewis Mansell and Hyuga Tanner.
The Austrians opened the scoring after just two minutes when a cross from the right was bundled home.
Despite being a man light, the young Rovers worked tirelessly, but a second goal for Rapid seconds after the restart made the task all the more difficult.
Rapid Vienna were then reduced to ten men themselves midway through the second half, but although Rovers battled hard for a way back into the game, they couldn't grab a goal their determination and perseverance deserved.
Rovers ended the tournament a hugely creditable third place, behind winners Spartak Moscow and runners-up AS Monaco.
ROVERS: Fisher, Askew, Platt, Nyambe, Tomlinson, Hardcastle, Doyle, Edo, Faws, Howarth.