Everton managed to pick up a 1-1 draw with Liverpool at Anfield yesterday.
Carragher was critical of Everton’s tactics, at times, and suggested that they were sitting too deep.
But Allardyce claims that the Toffees were forced back by Liverpool’s quality.
He said: “You get forced back, if Jamie’s listening to this, by two teams. “One is by the talent of the opposition and the failure of your players to play out when you get possession. I will give him a lesson on coaching so he can understand next time he is commentating.”
Everton were largely on the back foot at Anfield, but they still picked up an impressive draw.
The Toffees did ride their luck at times, with Liverpool missing some big chances, but they held firm and were rewarded with a penalty, which Wayne Rooney dispatched with ease.
Everton are still yet to lose a match since Allardyce took charge, with the 63-year-old boss quickly getting the Merseyside club organised.
Everton have now moved up to 10th in the Premier League table, and they seem to have put concerns over relegation to bed.
Everton are next in action on Wednesday, when they take on Newcastle United at St. James’ Park.
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