Cole was sent off on the stroke of half-time for a challenge on Arsenal debutant Laurent Koscielny in their season opener at Anfield on Sunday but Carragher says the difference the former Chelsea man has already made at the club bodes well for him to return strongly after he serves his three-match ban.
"Joe has lifted the whole city," said the Liverpool vice-captain. "It's not just in the dressing room, it's the whole place.
"He's staying in the centre of town, getting well-wishers all the time, and he's starting to realise how big this club is.
"He's like a God in the city already, so he's already got the fans on his side.
"Joe is the type of player others love playing with. We saw that in Europe with Stevie (Gerrard) and with (Fernando) Torres that'll come.
"I'm just disappointed for him that it ended like that. You see that tackle so many times, trying to block a ball down the line, and if you don't get the ball, you can't stop yourself in mid-air. To me, that type of tackle should be a yellow."