Sterling reportedly turned down a deal worth around £100,000-a-week and confirmed in an interview this week that he will not discuss a new deal until the summer.
The England forward's decision has led to intense speculation over his future with top four rivals Arsenal, Manchester City, Chelsea and Manchester United all linked.
But Carragher has described Sterling as "desperately naive" for his stance and claimed he would not get into the Arsenal due regularly due to competition.
He said in his Daily Mail column: "He was desperately naive to say such a thing on the eve of such a crucial game.
"He is also naive, as are his advisers, if he thinks Arsenal would guarantee him a regular place every week.
"What Sterling’s camp are struggling to see is that Liverpool is the best place for him. Forget money for a minute. This is about football and his development.
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Jamie Carragher was angry at Raheem Sterling's comments
"He will start the vast majority of games at Anfield. Would that be the case at Arsenal? No.
"He wouldn’t play as a centre forward there ahead of Olivier Giroud or Alexis Sanchez.
"Being a No 10 would be out of the question, as he is not like Mesut Ozil or Santi Cazorla, which would mean a battle with Danny Welbeck and Theo Walcott to start wide right."
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