Dalglish's position at Anfield has been under the spotlight recently as the club parted ways with director of football Damien Comolli due to a poor season on the pitch.
Despite an apparent reshuffling behind the scenes, chief executive Tom Werner claimed that the Scot's position was not at risk.
Carragher has now insisted that Dalglish has been unfairly criticised for the team's disappointing league form.
"For me, he is the most iconic figure in British football," the defender told The Telegraph. "You have great players and great managers and he is in both camps. Stein, Busby, Ferguson, Paisley, Shankly, Clough, Dalglish - they're all the great managers. And he is in with all the great players as well. No one else is in both camps.
"If Liverpool aren't doing well and you are manager then you are going to get criticism. That's the price on the ticket and we all accept that to a certain extent, but I think some of the criticism towards the manager in recent weeks has been a little bit disrespectful and crossed the line because of who he is.
"I'm not saying that should absolve him of any criticism, but some of it has gone a little bit too far. Considering what he has done in the game and what type of figure he is there should be a little bit more respect out there."
Liverpool take on local rivals Everton at Wembley Stadium later today (Saturday) in the first of this weekend's FA Cup semi-finals.