The Reds commander has taken some criticism for not leaving the Merseysiders, but Carragher has hit back at those doubters and claims that they do not realise how big a club Liverpool is.
"Steven Gerrard was good enough to play for Barcelona and Real Madrid," Carragher told talkSPORT. "People always said to me 'you're loyal to Liverpool' but I don't think about it like that. I'm happy to be at Liverpool. Steven's loyal to Liverpool because he's had the chance to join some of the biggest clubs in the world and play with some of the biggest players [but has decided to stay].
"Sometimes people outside the club forget how big Liverpool are. I know at the moment we're not in great shape but we're trying to build up again. We've won the European Cup five times, wherever we go on away games or pre-season tours, we're a massive draw and massive name in the world of football.
"I can understand what Zlatan Ibrahamovic was saying. He wasn't saying that he should have left to win a league title. I think he was saying he would have liked to see Gerrard play for Barcelona or Real Madrid, because a lot of the best players in the world go to those clubs. It was more of a compliment really.
The loyalty that Steven Gerrard has shown Liverpool, you don't see that anymore in the modern game. It's something that should be applauded, certainly not looked down upon."
Liverpool host Wigan Athletic in the Premier League on Saturday.