With the game goalless, after 51 minutes, Wales midfielder Aaron Ramsey appeared to be caught by Dwight Tiendalli as he broke into the Swansea penalty area.
Referee Howard Webb turned down the appeals, with television replays suggesting Ramsey had caught his own trailing leg as he chased the ball.
At the outset, even Swansea manager Michael Laudrup feared that Webb might have got it wrong.
“On the bench my initial reaction was that it was a penalty, but I have not seen it again after the game,” said the Dane.
Arsenal manager Wenger told reporters: “It was a penalty and the referee saw it. You know why he did not give it?
“Because he thought the guy (Tiendalli) had not done it on purpose, and I think as well it was accidental, but he did not trip himself — he was caught clearly by the leg of the Swansea player.
“The referee hesitated and he did not give it.”
Wenger felt his side had done enough to win Sunday’s game, which saw Danny Graham net an 87th-minute equaliser for the hosts after Michu’s opener had been cancelled out by Lukas Podolski and Kieran Gibbs had put Arsenal ahead.
He added: “We should have won the game. The first half was a bit locked and one-paced, but the second was much more open.
“Unfortunately I felt on the corner just before their (second) goal, we lacked some calmness and focus.
“I am frustrated as I did not want a replay, but if it’s the choice between staying in or going out, then I would rather take the replay at the Emirates.”
Laudrup agreed with that assessment, saying: “A replay is not exactly what I’m looking forward to, with the two Chelsea (League Cup semi-final) games in mind and league games.
“It is very tight, but when you have been in this profession at the highest level, you always want to play and win.”
Laudrup will spend Monday speaking to those players who have been linked with possible moves away from the Liberty Stadium, including Graham.
“I am going to speak to all players who are not playing regularly,” said the manager.
“Danny is playing well and is important for us because he is scoring goals, but let’s see what he says.
“If I am talking to the players, it does not mean I am telling them they can leave.”
As far as the game was concerned, Laudrup said: “I think the overall feeling is that it was a fair result. In the first half, Arsenal had only one or two shots at goal and we went closest with a shot from Danny Graham.
“In the second half we made a couple of changes that paid off, with Michu’s goal, but to be fair to Arsenal, they put us under pressure, they kept the ball, took over possession and in those 15 minutes, we lost the ball too much.
“They did not score in that spell and I thought we would win 1-0, then they scored two very late goals. But again we came back and we showed the character of our team to come back and score the equaliser.”
The winners of the replay will face a trip to second-tier Brighton and Hove Albion, who bundled Newcastle United out of the cup for the second season in succession on Saturday.