Manchester City lost 2-1 to the Gunners yesterday to slip four points behind the north Londoners, and six behind log leaders Leicester City.
And although Toure netted with a brilliant strike eight minutes from time, Carragher was less than impressed with the Ivorian's efforts at the Etihad.
"I think it is a joke to be honest," Carragher said in his capacity as a Sky Sports pundit on Monday Night Football. "I mean the goal is just a great goal, that is nothing to do with running, or different things.
"It wound me up the fact that he got the goal at the end and in commentary Davie [Provan] was saying: 'He has run the game the last 20 minutes.'
"It is like he comes alive because he thinks, 'We have got a goal and have a chance of me getting a bit of glory and being involved'."
Carragher questioned why City coach Manuel Pellegrini effectively detailed Toure to police in-form playmaker Mesut Ozil, rather than the more energetic Fabian Delph.
"They lost the game tonight and one of the major reasons was the space Ozil had behind him. Now it is nothing new, I am not saying anything we have not said the last two or three years.
"But it just comes back to that fact that he just wants to switch it on when he thinks he can get a goal. And you talk about one of your major players, your leaders in a dressing room, that is unbelievably selfish the way he has played tonight.
"I think Yaya can still bully teams from central midfield, especially at home, but these games - why did you buy Fabian Delph? You buy him for those games, that energy, that aggression in central midfield.
"You are playing against one of the best players, one of the most creative players in Europe tonight, and you put Delph on the left to look after Arsenal's right-back. I could not believe it before the game.
"And then what we have seen in the game, I am not saying it proved me right, but I could not believe it - Yaya Toure can look after Ozil? You know that before the game, you did not need the proof tonight that he was going to let him go free," concluded the ex-England international, who made 737 appearances for the Reds before retiring in 2013.
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