The 22-year-old unwittingly found himself the focus of attention in the warm-up to England's Euro 2012 qualifier against Wales this week when national team boss Capello, not for the first time, questioned his fitness and off-field attitude.
Carroll failed to make the bench for the previous match last Friday in Bulgaria and only made a last-minute substitute appearance at Wembley.
He missed England's Euro 2012 qualifier against Switzerland at the end of last season - and the European Under-21 Championships - due to injury and was pictured partying on holiday in Barbados during the summer.
It prompted Capello to describe the player's lifestyle as "a private problem", adding "If he wants to be a good player and a good sportsman, he needs to drink less than the others."
Understandably Dalglish, who spent £35million to sign the Newcastle forward in January, defended the player and reiterated his support.
"For us, as we've said often enough, it falls on deaf ears, Andy wasn't properly fit last year because of a knee injury," said the Scot.
"We've been very pleased with his level of fitness this year because he's lost that knee injury.
"I think his fitness now would stand up against anybody's and we are delighted with the progress he has made.
"I don't know how much the media is going to milk this, the story goes back to March.
"You don't know his lifestyle. Who knows his lifestyle? Andy.
"I think Andy is wiser than a lot of the people who write about him and I don't think his lifestyle is anything like they'd like it to be to get stories."
Dalglish added: "Andy is very appreciative of advice from anybody that's got a good standing in football.
"I think he appreciates Fabio Capello's advice. He's got great respect for Fabio Capello - and I think Fabio Capello has great respect for Andy Carroll."
The Reds boss was pleased to see all his international players return to the club's Melwood training ground without having sustained significant injuries while on duty for their countries.
Charlie Adam was released from Scotland's squad prior to their match at home to Lithuania because of a hip problem but he is expected to be fit for Saturday's trip to Stoke.
There was also further good news, with right-back Glen Johnson in contention for his first Barclays Premier League appearance of the season having been injured in the final pre-season friendly against Valencia.
And captain Steven Gerrard, who has not featured at all since a groin operation in March, is edging ever closer to a long-awaited return.
"I think we've been pretty fortunate," added Dalglish.
"There doesn't appear to have been anybody come back with any injuries.
"Charlie should be all right for the game. I think it was right what (Scotland manager) Craig Levein did in not playing him on Tuesday.
"To get him back was commendable of Craig Levein.
"Glen Johnson is training alongside us again now and Steven is getting closer every day, so everything on the injury front seems to be pretty positive for us at the moment.
"When Steven is ready to come back it will be a fantastic boost for everybody.
"The transfer window is shut so for us it will be a real bonus because it will be like a new player coming back.
"As he said himself in an interview on Saturday, everything feels really strong, fresh and he's happy with where he's got to and what he's done and we're delighted for him.
"He deserves a break from injuries and he'll be welcomed back with open arms."