The club's £35million record signing's performance in Wednesday night's 1-0 Carling Cup semi-final first-leg victory at Manchester City came in for some criticism because of his ineffectiveness.
Carroll squandered a golden chance to put his side ahead in the fifth minute when he turned Stefan Savic on the edge of the penalty area only to fail to beat goalkeeper Joe Hart who saved with his legs.
But after flashing a long-range header wide of the far post from Martin Kelly's cross the England international's night became increasingly frustrating.
With his team holding on to the lead given to them by Steven Gerrard's 13th-minute penalty the 23-year-old became more and more isolated up front and as his job became harder his confidence dropped and his annoyance rose.
To be fair to Carroll, towards the end of the game Liverpool dropped so deep when they did manage to get the ball up to him there were no team-mates within 40 yards.
It was not the way a man who has scored just four goals in 23 appearances wants to be treated but Dalglish praised his big front man, for whom speculation about his future refuses to go away, for his contribution.
"Andy worked fantastically hard for us and sacrificed himself for the sake of the team," said the Scot.
"If our players continue to work as hard as he did last night [Wednesday] - every one of them - then if we want to move in the right direction that will be a great start for us.
"And in the second half they sacrificed their own beliefs for the benefit of the team and they defended really well.
"There is nothing wrong with the commitment of this squad and if it were going to be put to the test it was going to be at City and they stood up to the test.
"There weren't many too many near misses for City and every single one stood up and was counted and sacrificed themselves for the team and I think everyone will have appreciated it."
With Luis Suarez banned for a further five matches Carroll is likely to get his first extended run in the side and he faces Stoke at Anfield on Saturday looking for his first Barclays Premier League goal since the end of October - although he did score in last week's 5-1 FA Cup win over Oldham.
One player who has had no trouble finding the net has been captain Gerrard, who at the Etihad Stadium made it four goals from as many starts in an injury-troubled season.
He has now scored back-to-back penalties and made it successive 90-minute outings after three short substitute appearances after two months out.
Dalglish believes the midfielder, having come back from a groin operation in March and then an ankle infection, will have a major impact on the side in the final four months of the season.
"For Steven to step forward and score with a penalty is great for us," said the Reds boss.
"He is going to get better every time he finishes a match.
"He is certainly gaining the benefit. It is great to see him back and he has a great influence for us."
Gerrard has spoken previously about what a bad time 2011 was for him but he now feels he is back where he belongs.
"I feel like a footballer again - I've had a difficult year," he told BBC Sport.
"It's games like this (against City) that I've missed, games like this I've been patient for and worked so hard to get back for."