Robbie Keane came off the bench to level things at 1-1 after 90 minutes following Henri Lansbury's opener, but Nasri won and converted a penalty shortly after the start of extra time to put Arsenal 2-1 up.
Nasri then converted another penalty before Andrei Arshavin rounded off the scoring, but Redknapp feels the first penalty should not have been given.
He said: "I thought the first one was harsh. He fell over. Really I think he dived for the first penalty."
Nasri had previously resisted taking penalties where he had been fouled but, after Tomas Rosicky blazed over the bar against Sunderland on Saturday, he decided to step up to the spot at White Hart Lane.
"I provoked the foul and then I didn't take the penalty," Nasri said, "but after I talked with the boss and said, 'Next time I will take the penalty', and I scored."
Arsene Wenger added: "He had a superstition to think that when a penalty is made on you not to take it, but I tried to prove to him that that's solely based on fear. He realises now that it was a bad superstition."
Wenger, who served a one-match touchline ban, felt his players were far superior on the night. "I felt that we dominated completely," he said.
Wenger had named a strong side for the tie and he said: "We have got a few reproaches that we did not take the competition seriously. It was a derby and to go out straight away for us would be difficult.
"We have a momentum going, and it was important not to interrupt it, also some players needed competition."
He added: "If everybody is fit, I can go as well for this competition. I have always said that the big competition you really count are the Champions League and the [Premier League] championship.
"I maintain that, but it doesn't mean I don't celebrate when we don't win game. I want to win every single game I play with my team."