The right-back confirmed his impending departure on Monday, ahead of a widely anticipated move to Real Madrid.
However, he was repeatedly booed while in possession during the second half, as Arsenal battled back from two goals down despite finishing with 10 men following Mikel Merino's late red card.
"That's the story of the game. That's what we will be talking about after the game, and the back pages of every newspaper tomorrow," said Carragher.
"I'm surprised how many. When you're in a crowd of 60,000, there's no doubt there are a lot of unhappy people at Liverpool about the situation, and I've said that's understandable.
"But for me, I don't believe that any player putting that red shirt on, going out to play for the club and trying to win them points or win them trophies should be booed.
"I understand, there's a lot of ill-feeling, and some people outside of Liverpool won't be able to understand that. I do.
"But booing one of your own players while they are playing is not for me."