"I don't think so, no," said Wenger when asked if their shoot-out defeat was all in the mind.
"You feel embarrassed when you don't give everything. I feel the team did fight and will be more disappointed and frustrated."
Wenger didn't put the defeat down to a lack of effort either, quoted on the official Arsenal website as saying:
"I feel we gave a lot. It's difficult to make the game the whole time.
"We played with a very offensive team. What is disappointing is [we played] basically over an hour with five strikers basically, and couldn't score. We created a lot of different situations.
"You have to say they defended very well. It's difficult to play this kind of game. I know people will say 'it's League Two', but a cup game is a cup game.
"In football you always have a chance if you give everything. They did that tonight and we put ourselves in a difficult situation by being 1-0 down."
While most of the attention will understandably be on Arsenal's failing, Wenger did praise their League Two opponents.
"It's disappointing, but congratulations to Bradford. They defended well [and] started stronger than us. In the second half of extra-time it was all us but we couldn't convert our chances. They defended very well."