The Togo international scored a brace in his first start this season as Spurs beat Southampton 3-2 on Saturday which prompted plenty of positivity but that was met with derision by a scathing Carragher.
"For me, a player like him, he should be one of the best players in the world. why isn't he? He's got everything. He can play up on his own. He can play up with a partner.
"You can criticise AVB (ex-Spurs boss Andre Villas-Boas) for putting him in the reserves, but (Arsene) Wenger got rid of him, (Roberto) Mancini got rid of him, AVB tried to get rid of him, I'm sure if (Tim) Sherwood, at the end of the season, or if a new manager comes in, will try and get rid of him."
Carragher added: "So let's not get too carried away with Adebayor. For me a player like that is a disgrace, really. If he can play like that with that ability, why isn't he doing it every week? He should be. Why isn't he like Didier Drogba?
"So he comes in for a few games, does well and everyone's saying how great he is. AVB should have played him a lot more, should have done this. Why can't he do this every week?"
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