Carragher feels Liverpool's public image took a battering towards the end of the Benitez regime, as the former Anfield boss found himself at odds with rival managers.
"I care about the club and it concerned me that, last year, people just didn't like Liverpool," he said.
"Other managers hated us and stuff in the media was all negative. We weren't doing well on the pitch, to be fair, but it was just negative Liverpool all the time.
"I'm not getting involved in what the causes were, but we need to get back to behaving in a way that wins respect."