Carragher, speaking on The Overlap, likened Palmer to his former teammate Steven Gerrard.
"I commentated on Brighton vs Chelsea in the league a month ago. I'm a big fan of Cole Palmer, and he played two passes early on, but the longer the game went on, you could see the frustration with his team-mates," said Carragher.
"It reminded me of Stevie (Gerrard) at Liverpool at times, because he was so much better than everyone else and he got frustrated. Stevie was a local player, but he was never going to leave, whereas Cole Palmer isn't.
"This is when I go back to those eight-year contracts, and whether they are good for the club and players.
"If you're Cole Palmer, who's got six or seven years left on his deal, and he should be playing for a team looking to win the Champions League, how does he get out?"