After a two-month investigation, Suarez was given an eight-game ban by the Football Association on 21 December. A day later, Liverpool wore 'Suarez 7' T-shirts in the warm-up before their Premier League game against Wigan.
Carragher said the club "got it massively wrong". The former England defender was working in his role as pundit on Sky Sports on Monday alongside ex-Manchester United full-back Evra.
Carragher said: "There is no doubt we made a massive mistake; that was obvious. We got to the ground, had our lunch and then had a team meeting - I don't know if it was the manager [Kenny Dalglish] or [coach] Steve Clarke - asking one of the players if he was still wearing the shirt, and that is the first I had heard of it.
"I am not lying and saying I wasn't part of it because as the club we got it wrong, and I was vice-captain. I am not sure who was actually behind it. I don't think it had anything to do with the manager Kenny; I think it was the players who were close to Luis in the dressing room, who really wanted to support their mate.
"Maybe I have to look at myself now and say I did not have the courage as an individual to say 'I am not wearing it'. I don't think everyone within Liverpool Football Club thought what we were doing was right but I do think as a football club, or you as a family, your first reaction is to support them even if you know that they are wrong, and that is wrong."
Evra added: "When I saw it I was like, this is ridiculous. This is unbelievable. You put your own club in danger when you do those things. You always have to support your player because he is from your team but this was after the ban. If it was before and we were waiting for the sanction, I would understand,” according to bbc football.
"What message do you send to the world? Supporting someone being banned because he used some racist words," Suarez added.