But Wenger, who last won a trophy in 2005, refused to accept that he and his players should be deeply embarrassed by this latest setback.
"You feel embarrassed when you don't give everything but I feel the team did fight and they will be more disappointed and frustrated," said Wenger.
"It was a typical English cup game on a difficult pitch and overall we lost on penalties but I cannot fault the efforts.
"We kept going until the last minute and in the end Bradford got on top of us. Of course we missed three penalties and that's a lot to take."