He was also far too big for his boots.
Peter Crouch has spoken on his podcast about how Gerrard and Carragher would basically decide if they'd like a player after one or two training sessions. He spoke about players being finished at Liverpool after their first training session. But he was speaking about it as a good thing; standards, and all that. But read between the lines, and what he was talking about was a captain who wasn't interested in his team mates well-being unless he deemed them good enough.
His attitude to new signings was never 'I'm the skipper, I'll do everything I can to help this new player settle in.'
Basically, during that period, if you weren't of the Alonso, Torres, Suarez ilk, and didn't show it almost immediately in training, then you would be treated like you didn't belong.
No surprise they've been a much better team since he hung his boots up. His 'all about me' attitude held them back for years.