The holders looked set for a sensational return to the final, where they stunned Manchester City 1-0 last year, when Jordi Gomez broke the deadlock at Wembley with a 63rd-minute spot-kick.
But Arsenal defender Per Mertesacker, who fouled Callum McManaman to set up that opportunity, levelled for Arsenal with eight minutes of normal time remaining and Gary Caldwell and Jack Collison were unable to repeat Gomez's composure from 12 yards in a 4-2 shootout loss.
Rosler, whose team dumped out three Premier League teams on their way to Wembley, suggested there will be a change of plan if Wigan return to the national stadium in the Championship play-off final next month.
The former Manchester City striker told reporters afterwards: "I got asked 'have you practised penalties?' I said, 'No, I am German, you know we don't need to practise penalties'.
"We want to be back here in May. When we are back in May, then we will practise penalties."
Rosler was delighted with the efforts of his players, who have stormed towards the Championship play-offs since he replaced Owen Coyle in the DW Stadium hotseat in December.
"I couldn't ask for any more than what they've given me, not only today but since I walked through the door at the football club," he added.
"Today we faced Arsenal, one of the top teams in the country, and we did very well.
"We had to make a few substitutions too early and unfortunately we couldn't hold out. We forced Arsenal to play long in the second half. All credit to my boys. We still looked to counter and attack them when we could.
"I'm absolutely proud of how they performed and what they put in.
"We have to recover. We'll be walking out of Wembley on paper as losers but in our minds as winners."
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