Everton were beaten 4-0 by Liverpool at Anfield yesterday.
With Everton 2-0 down against their Merseyside rivals, Funes Mori put in a terrible tackle of Divock Origi and was handed a red-card.
On his way off the pitch, Funes Mori grabbed the Everton crest, but Carragher was less than impressed by the defender’s actions.
"I was made up he went off in some ways because it helped Liverpool get more goals, but why was he kissing the badge,” Carragher said.
"Number one, he has only been here for two minutes and number two, why is he playing to the crowd because he has injured a Liverpool player? Are they going to be happy with that?
"They were getting battered in the game and he's now going to miss the biggest game of the season when they've got Jagielka out.
"It's embarrassing. What is he doing? Everton fans won't fall for that nonsense.
"It was the only challenge anyone put in by the way, but it was a bad one.”
Liverpool had been the better team before Funes Mori had been dismissed, but they were totally dominant after he left the field.
The Reds scored two further goals through Daniel Sturridge and Philippe Coutinho, to round off a comprehensive 4-0 victory.
In truth the scoreline could have been heavier, had Liverpool been more ruthless, and the pressure is now firmly on Toffees boss Roberto Martinez.
Funes Mori’s red card in the Merseyside derby means that he will now be suspended for Everton’s FA Cup semi-final against Manchester United at Wembley on Saturday.