The Liverpool striker has received much criticism since his transfer from Newcastle, but the man who took him to Anfield said he showed his true ability against Sweden
Carroll has come in for a large amount of criticism since Dalglish signed him for £35 million in January 2011.
He opened the scoring for England with a fine headed effort against the Swedes on Friday, and Dalglish said he was never in any doubt about the 23-year-old's ability.
"Andy Carroll gave something close to the complete centre-forward's performance in Kiev on Friday night," Dalglish told The Mirror. "He scored a magnificent header, he held the ball up well and he worked back and made some vital clearances.
"I have always said that the big man has an awful lot more things going for him than against him and he proved that against Sweden.
"The vitriol that has been aimed at him over the past year or so is running out of steam. Even a couple of days ago, I heard someone had written that fans were laughing at him. I think Andy will be the one who is laughing now.
Dalglish added that he always knew Carroll would come good, and that England were starting to see the rewards of the hard work the frontman had been putting in at club level.
"I don't have any feelings of personal vindication about the goal he scored. Some people may have questioned my decision to buy him for Liverpool but it's not about me or any of the criticism I have received.
"Whatever anybody else said, he was always going to come through as a player. His attitude and his determination when he played for me at Liverpool were there for everyone to see.
"If he had any problems, it was not really because he was struggling to settle in. It was because there four or five new signings and the existing players were adapting to them.
"The kind of performance he produced for England in Kiev proves that he is starting to get the benefits of the work he did at Newcastle and Liverpool."