The Frenchman went down under pressure from Sebastian Bassong and then picked himself up to give the Gunners a 2-1 lead early in extra-time after the north London derby finished 1-1 after 90 minutes.
Redknapp said: "I thought the first penalty was harsh. I thought Nasri dived.
"The second was blatant. It was Caulker's first appearance anywhere near this level and was a good experience for him."
Bassong agreed on the first spot-kick, adding: "He went down too easily, I didn't think it was a penalty.
"He told me afterwards that I barely touched him.
"It leaves a bad taste in my mouth. I touched Nasri's chest but I did not grab him. I have seen the video and from my point of view it was not a penalty."