"It was a lot of money but I need to do what I have to do to prove the money was worth it," he said at a news conference to unveil himself and fellow striker Luis Suarez.
"I am here to score goals and create chances for the team and that is what I can do.
"I have scored goals at Newcastle and that is what I want to bring here - we'll just have to wait and see [whether the transfer fee was worth it]."
Reds manager Kenny Dalglish added that he had no qualms about the fee he paid for Carroll, who arrived at Anfield carrying a thigh injury.
Dalglish also took the opportunity of the news conference to take a swipe at the media, who he felt had been unfair in their reaction to Carroll's arrival.
"I'd like to reassure Andy we are more upbeat about Andy coming than I think yourselves [the media] are, because every question seems to have negativity in it," said Dalglish.
Dalglish 'disappointed' with Torres exit
"We have no reason to be negative about Andy signing for Liverpool. It is a great signing for us, as Luis's is.
"We will look forward to getting him fit, up and ready for work and he'll play when he's good and ready."
Despite claim and counter-claim about the means of his departure from St James' Park, when pressed on Thursday Carroll brushed aside questions over his exit saying he would prefer to focus on making a fresh start at his new club.
"I have got massive respect for Newcastle and it is my team and my home club and I'm not really going to talk about what happened at Newcastle," he added.
"It means a lot to me but I am a Liverpool player now and that is what I have to concentrate on."
Carroll, who has one England cap, says he is still unsure of when he will be ready to return. But he adds that when he does, only then will it truly hit home that he is a Liverpool player.
"I'm working hard at the minute in the gym at Melwood," said Carroll.
"I need to get my fitness up and when I finally make my debut with the number nine that's when it will hit home that I'm here and I'm here to stay."
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