The Premier League side lost 3-2 on spot-kicks to the Bantams, who play in League Two, after they drew 1-1 after extra-time.
But their French manager has insisted his players gave it their all in what was a tough cup match at Valley Parade.
Wenger said: “It was a typical cup game on a difficult, but playable, pitch and overall we lost on penalties but I cannot fault the effort they put in. They gave everything until the last minute.
“I feel we gave a lot. We played with a very offensive team, what is disappointing is that basically over an hour we played with five strikers and couldn’t score but we created a lot of chances.
“It’s difficult to play this type of game. I know people will say it’s [against a team in] division four but a cup game is a cup game and in football you always have a chance if you give everything and they did that tonight.
“You feel embarrassed when you don’t give everything but I feel the team did that and they will be more disappointed and frustrated.”