The FA Cup holders continued their defence of the famous trophy with another Premier League scalp, while Cardiff continue to struggle under Ole Gunnar Solskjaer
Goals from Chris McCann and Ben Watson either side of a Fraizer Campbell equaliser were enough to send the Latics through to the last eight, with another Wembley appearance only 90 minutes away.
And Rosler was full of praise for his in-form squad, claiming that the players had made their supporters proud.
"I'm very happy with our performance," the German told reporters.
"We made the supporters proud. We wanted to. We've had the toughest programme in the country but our supporters travelled in great numbers."
Watson was the Wembley hero last season as he scored the injury-time header to defeat Manchester City and win the cup for his side.
Watson scored again today and Rosler said: "I didn't see Ben Watson's goal. I turned my head for one second, and the next thing I knew it was in."
Meanwhile, on-loan midfielder Josh McEachran took to Twitter to express his delight at the victory after being introduced in the second half.
He said: "Great win for us! Fans were great again. Looking forward to the next game."