Villa, who have won only one of their last seven league matches, were blown away by a fine Bradford performance at Valley Parade, leaving them with it all to do back at Villa Park.
"At any level of football, you can't defend set-plays like that and expect to win games of football," Lambert said.
"But we're still in the tie, absolutely. It will be a different game at Villa Park. We had lots of chances to score and we never took them but it's only half-time.
"It will be a totally different game at Villa Park but when chances come our way we have to take them.
"But you've got to give Bradford credit, they defended resolutely and their goalkeeper made some good saves."
Bradford manager Phil Parkinson admitted his players had far exceeded his expectations.
"I was asked before the game on the TV, would we take a draw? I said `yes'," Parkinson said. "Obviously we would have taken a draw.
"We didn't set out to get a draw, we actually set out to win the game, but if we had been going there with a draw it wouldn't have been the worse scenario in the world."