The 22-year-old striker, a prolific goalscorer at his home club Newcastle United, became the most expensive English player when he was brought for 35 million pounds on Monday to replace Fernando Torres.
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Carroll, who has scored 11 league goals this season, was asked whether he felt he was worth the money.
"I'm sure that time will tell really," he told a news conference. "I've scored goals at Newcastle and that is what I want to do here. We'll just have to wait and see."
Dalglish stepped in to defend the fee paid for Carroll, who will not make his debut for a few weeks because of a thigh strain he was carrying before he joined on the same day Liverpool signed Uruguay striker Luis Suarez.
"Every question you ask is negative, we don't see any reason whatsoever to be negative in any way shape or form about Andy Carroll signing for Liverpool Football Club," Dalglish said.
"It is a great signing for us. We can reassure Andy that we are more positive than what yourselves are.
"The price might be a bit more than what some people think it should be but every single person in here has got to justify their wages and their costs so if you can do that for yourselves then I'm sure he can do that for us," he added.
DIFFICULT LIFE
Dalglish urged people to remember that Carroll, who last year pleaded guilty to assaulting a man in a nightclub, was only young.
"When you get older you realise some things you've done might not be correct but everybody has a story to tell and everybody wishes they had done something different," he said.
"You have to understand it's a difficult life for footballers to adjust to being in the limelight.
"They go from being 16/17 years of age... to being transferred for 35 million, it's a huge change in your life and I'm sure he'll handle it very well. His innocence is quite endearing."
Carroll said it had been tough leaving his home city and while his strong local accent will probably never leave him, he was already feeling settled in the north west.
"It just feels really like home now, even though it's only been three days," he said.
His future partner Suarez made a dream start by scoring on his debut in Wednesday's 2-0 home victory over Stoke City in the Premier League as Carroll watched from the stand.
Wearing the number seven shirt Dalglish himself sported during his Anfield playing days, Suarez said he felt no extra pressure to be wearing such a famous jersey - mainly because he had no idea of the significance when he picked it.
"To be totally honest, when I saw the list of squad numbers available I chose seven because I chose the seven, it was
