Carroll turned in the opener from close range in the 71st minute to end a drought of more than 11 hours worth of playing time without a goal, before Luis Suarez sealed the victory eight minutes from time.
"Obviously it will be a boost for him to get his first league goal but I don't know what all the fuss is about,” Dalglish told reporters. “We are delighted with him. He has worked really hard in training and he deserved it.
"Andy has been fantastic, his stats in training are better than most peoples so I don't know what the fuss is about. The price-tag is irrelevant and has nothing to do with his form or performances. He is just as important to us as [Jay] Spearing, [Steven] Gerrard or [Jamie] Carragher, who cost us nothing."
Gerrard continued his return from a groin injury after replacing Charlie Adam in the 67th minute and could now be in line for a call up to Fabio Capello's England squad for the crunch Euro 2012 qualifier against Montenegro.
Dalglish is pleased with the progress the Liverpool captain has made in his recovery but endorsed a view expressed by Gerrard on Friday that he is probably not ready to play for England.
“It's another step forward for Steven, coming on in the derby and getting some games under his belt,” Dalglish said. “He had no reaction after the game. Steven aired his views on England yesterday and I agree with him.”