Capello left Carroll out of the squad for England's Euro 2012 qualifier in Bulgaria on Friday and although he made a late appearance as a substitute in Tuesday's win over Wales, Capello told reporters he was concerned about the striker's drinking habits and general fitness.
Dalglish, speaking at his news conference at the club's training ground Melwood on Thursday before Liverpool play at Stoke City on Saturday, said he had no problems with Carroll, who joined for 35 million pounds from Newcastle United in January.
"As we've said before Andy was not properly fit last season because of a knee injury but we have been pleased with his level of fitness this season because he has lost that injury," Dalglish said.
"I think Andy is very appreciative of advice from anyone who has a good standing in football.
"I think he appreciates Capello's advice because he has great respect for Fabio and Fabio has great respect for Andy."
Carroll, who has played three times for England and scored once, missed the final qualifier of last season against Switzerland and the European Under-21 Championships due to injury and during the summer he was pictured partying on holiday in Barbados.
Capello said before the game against Wales: "Andy needs to be careful. I don't know anything about his lifestyle. It is a private problem that I never spoke about.
"But if he wants to be a good player and a good sportsman, he needs to drink less than the others. He is not at the top of his form at the moment."
Carroll is one of nine new arrivals at Liverpool since January and Dalglish said he was delighted with the squad he has assembled since he took over at the start of the year.
"We've always had selection problems but as we've said before, I think the quality of the squad we have is better than it was last year.
"It is not a team that wins trophies, it's a squad and the stronger our squad is the better chance we have of coping with the problems that come up throughout the season."
Liverpool have made a bright start with wins over Arsenal and Bolton Wanderers after an opening day draw with Sunderland. Only Manchester United and Manchester City are above them in the table.
