The 23-year-old striker, who arrived at Anfield on January 31st last year for £35 million from Newcastle United, scored the first goal of the game at Molineux before Craig Bellamy and Dirk Kuyt wrapped the match up.
After the match, Dalglish revealed he was delighted with the entire team but singled out Carroll for his performance.
“We're pleased with everybody. It was a great finish for the first goal,” the Scot told reporters.
“[It was] a great ball in from Charlie Adam and a great finish from Andy, who played really well.
“He's a Liverpool footballer and he will make a contribution for us many times.
“He flicked on one on Saturday for Dirk Kuyt to score against Manchester United and did the same for Craig Bellamy at Bolton.
“If [Carroll] gets a goal he gets a goal, but his contribution is fantastic.”
The victory was the third big result in seven days for the Merseyside club, after they sealed a League Cup final berth with a 3-2 aggregate win over Manchester City and secured a 2-1 FA Cup fourth-round victory against Manchester United.
Dalglish said of the performance: “I thought it was a very professional, high quality performance from the players, a fantastic reaction to the previous two games.
“This game became the most important one because it was the next one. They applied themselves well and got what they deserved. I'm delighted with everyone who played.
“It was great for Andy to score a goal. Craig scored a fantastic goal as did Dirk.”
Liverpool propelled themselves past Newcastle & Arsenal into fifth in the Premier League with the victory, and Dalglish lavished additional praise on Welsh forward Bellamy for his role in the win.
The manager continued: “Craig was fantastic. The wee man certainly has been fantastic for us. I wish his numbers were the other way around.
“Instead of being 32, I wish he was 23. He doesn't do anything that surprises you. He prepares himself well for matches.
“He does things for himself within the framework of the team. You expect something to happen.”