Wednesday pulled off a smash-and-grab win thanks to goals from Keith Treacy and Miguel Llera, which sandwiched Clayton Donaldson's second-half penalty for the Bees after he had been fouled by Owls defender Mark Beevers.
Rosler said: "I'm extremely proud of my players. They showed that we are very, very close to being in a strong position to challenge next season.
"We have built a very strong foundation this season and in this game I thought we were very unlucky.
"We had 16 shots on goal to their six and 60% of possession, but we just needed that little bit of luck."
Sam Saunders saw a free kick drift wide of the far post before Donaldson twice forced brilliant saves from Stephen Bywater and with time ticking away Karleigh Osborne blazed over from close range after a clever Douglas knockdown.
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