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 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."
Liverpool are now sixth in the table and Carragher believes the club can look forward to a positive future under new owners Fenway Sports Group, who replaced the unpopular George Gillett and Tom Hicks.
The 33-year-old defender, recently returned from a shoulder injury, added: "Of course we still have to improve on the pitch and that's something the manager will look to do in the summer.
"The supporters are a lot more onside and when we're all together - players and fans - as I've known for a long time, it can be pretty unstoppable at times and that's something we've probably not had for 18 months or so."
Carragher said: "I'd have loved him [Torres] to stay and I wish he would have given us to the end of the season. For two or three years for us he's been the best striker in the world.
"The disappointing thing is the timing of it but the start of the season hasn't gone well.
"I think it was something we were expecting either now or maybe in the summer. It's happened, good luck to him there and I'm pleased with who we've brought in. We've got to look to the future."