The Gunners were defeated 3-2 on penalties after three players missed their spot kicks, and the Frenchman blamed his side's inability to convert their chances for the defeat.
"I must congratulate Bradford, they had a good start then defended well," Wenger told Sky Sports. "What happened, happened with the penalty shootout. We had many chances, the goalkeeper had a good game and we could not convert them.
"There was no lack of quality, we did not convert our chances for different reasons. It was a real cup game."
Wenger did reserve some praise for the home side, which defended resolutely for the whole game and made life difficult for Arsenal throughout.
"We lost on penalties against a team that defended well," he continued. "I cannot fault the effort of the team. They gave everything, but credit to Bradford, it is part of the game.
"When you go out of a cup, it is never good enough for Arsenal."