Dalglish began a second spell as manager last month after the departure of Roy Hodgson, who endured a miserable six months at the helm.
Under Dalglish, the Reds have lifted themselves back into European contention with a six-game unbeaten run in the Barclays Premier League.
When asked if he was genuinely concerned, Carragher told talkSPORT: "Every day! To be honest, it's been like that for a little while.
"Stevie [Gerrard] and I are so involved emotionally, sometimes too much, and it affects your whole life, and the last 18 months have been really tough.
"We've not been doing too well and the fans are your friends and family and it takes its toll. So it's great that the pressure has lessened off and people are starting talking about the top four.
"Dalglish's presence and who he is has galvanised the whole club - players and supporters. I don't need to tell you what he means to the club and the fans."
Source: PA