Joe is like a god in the city after playing only half a game
The Kop centre-back said: "Joe has lifted the city. It's not just on the pitch or in the dressing room, it's the whole place. "He's staying in the centre of town getting well-wishers all the time, so he's starting to realise just how big a club this is.
"Joe is like a god in the city already and he's only played a game and a half." Carragher says Cole's red card for a rash tackle on Arsenal new-boy Laurent Koscielny during Sunday's 1-1 draw at Anfield should have been a booking.
However Liverpool have decided against an appeal and he will now miss the next three Premier League matches but is available for Thursday's Europa League play-off clash with Trabzonspor and the second leg in Turkey the following week.
He said: "You see the tackle he made 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 only a yellow. "He's going to be a major asset for us. He has already got the fans onside and was talking beforehand about how big a game this was for him."
And Carragher laughed off his son's preference for Cole. He said: "You don't want a defender's name on the back of your shirt, do you?"
Carragher reserves judgment on what the season has in store under new boss Roy Hodgson. He said: "We're Liverpool so shouldn't get carried away after drawing with Arsenal at home.
"People talk about last season but don't forget that the year before, with the same team, we finished second.
"We were never as bad as seventh. We're better than that. Maybe with a new manager and a couple of new players, we should be fighting for a top-four place. That has to be the aim."
Carra admits it was the right time for Rafa Benitez to go but refused to criticise him. He said: "I'd never do that. I've got too much respect for him. Everyone's different, with different ways of doing things.
"Everyone said the same about Gerard Houllier. I stuck up for him and I'll stick up for Rafa. "We had some great times but it was time for a change.
"Ever since I've been here, we've never been thought of as the best team in the country. We've enjoyed the chance to prove people wrong.
"I understand why people don't fancy us to get in the top four but we believe we can."
Middlesbrough keeper Brad Jones, 28, is set to join Liverpool after his club agreed to let him complete the move.
Jamie Carragher claims Joe Cole is a 'God' in Liverpool, but if so the man upstairs must have two left feet, as the new Anfield number 10 has had a shocking start to life at his new club.
Cole was sent off on Sunday for a truly silly scissors challenge on Arsenal's Laurent Koscielny. Then last night he saw a poor penalty kick saved against Trabzonspor. It was the first he had taken in a competitive match since he was 13. "I scored that one," Cole confirmed.
And if that were not enough, Cole was found guilty on Wednesday of speeding at 105mph and faces a ban, despite the best efforts of celebrity lawyer Nick 'Mr Loophole' Freeman. Quite a week.
Cole will have until next Thursday's return leg against Trabzonspor to stew over his miss, as he now serves a three-match domestic ban (and could be getting the bus to training).
No doubt Cole will say his faltering start is "just one of them things" but the fact is how you start can make a huge difference to your fortunes at a club.
It will take some time before Liverpool fans start getting on Cole's back. They tend to back their players even in the face of irrefutable evidence of decline (here's lookin' at you, Carra) and so they should - they are football supporters after all.
But the unrestrained jubilation that greeted the arrival of a Chelsea fringe player is just beginning to look a little misplaced. Diego Forlan's inability to find the net for 26 games (admittedly, most were as a sub) torpedoed his Manchester United career.
Even when he finally found the net he could not play with the freedom and self-assurance that has since enabled him to become officially the best player in the World (Cup).
Goalkeeper Massimo Taibi produced a sequence of horrific howlers, culminating in a legendary fumble that allowed a tame Matt Le Tissier shot to squirrel underneath his body. And that was that.
Ferguson said in his autobiography that although he still rated Taibi as a keeper, the Le Tiss error convinced the United manager to ditch him. Taibi's confidence, he reasoned, would never be the same again, and he could not visit an away ground without being reminded of the blunder.
The point is, a bad start affects both you and your opponents. You take the field anxious, rather than exuding calm confidence. They look at you in the tunnel and have a little snigger at that open goal you put into orbit last weekend.
Take Andriy Shevchenko, who began at Chelsea with two goals in three games but then saw his aura of invincibility slip over the next 26 games, during which time he scored just four times.
No longer did opposing defenders awe the man who routinely tallied 25 a season for Milan and won the 2004 Ballon d'Or. They had empirical evidence that he was actually a bit rubbish.
Jonathan Woodgate's Real Madrid debut was one to savour, and came over a year after he signed for the club due to injuries.
Woody powered a remarkable diving header into his own net, got sent off for two bookable offences and that was it: his reputation as a loveable clown was secured and his career at Real effectively over.
Early Doors could go on, but it won't bother as it is approaching its word limit.
Looking on the positive side, Mario Balotelli's debut goal at Timisoara could be the making of him. Even though it was just a tap-in in a Europa League qualifier that he nearly missed.
The same for Javier Hernandez after that ridiculous Community Shield goal that went in off his face. It was a goal - never mind how.
Like a golfer who has won his first Major, Balotelli and Hernandez have got over the hump. They can now relax and play with freedom.
As for Cole? He now has it all to prove and immediately finds himself under pressure. It's not terminal to his hopes of success at Liverpool, but it certainly doesn't help.