Wenger said: "We could do without it, 100%, but let's not complain because we play football. It's one more game to play. If that's the price we have to pay to stay in the hat, we're happy to do it.
"We are very short at the moment and cannot rotate very much. I could rest a few players today but not as many as I had wanted. I had planned to take Robin van Persie off but it didn't work that way."
The Arsenal boss recognised Cardiff had the better of the first half.
He added: "At 0-0 anything can happen but I wasn't too worried in the second half.
"Cardiff created more chances in the first half but they didn't really create many in the second. They wanted that replay because, when they had an opportunity to cross the ball at the end, they kept it in the corner. For them, maybe, it's a good opportunity to have another big game."
Some Cardiff fans had been unhappy with the decision to play for a draw in the dying moments but manager Dave Jones urged them to think again.
He said: "There were one or two boos in the last minute when we were keeping the ball in the corner but we were playing Arsenal so give us a break.
"We're at our most vulnerable when we're attacking teams, but I can't fault anyone today.
"We gave it a go as we said we would. With a little bit more composure or luck, it might have gone for us."
Cardiff are among the Championship play-off contenders and Premier League football would be a fitting debut for the new stadium that is due to replace Ninian Park next season.
But Jones insisted he wanted to keep the FA Cup run going, not least because of the money it would bring in.
He said: "My players would rather play than train. They're always moaning that they have got to train, so it doesn't really affect us. Arsene Wenger is fighting on three fronts at the moment so if he wants to give me the game, we won't go down to the Emirates although the chairman wouldn't be happy. It's a massive payday."