Carroll made a short debut appearance for the Reds in the 3-1 victory over Manchester United on Sunday.
“It was great to get out there and the result made it even better,” said the England international.
“I was on the bench and itching to get on right from the kick-off really but I’ve started now and can’t wait for the next game.
“When I was running back (after being called for a substitution by Kenny Dalglish) all the fans were shouting and screaming and so I got a little bit excited.
“I was over the moon to get on there and get back playing.”
Carroll was delighted with the support from Liverpool fans.
He told the club’s official website: “The support was unbelievable for me. The fans have been great since I signed and even when I was warming up, they were fantastic.
“It was an incredible atmosphere, definitely one of the best I’ve ever experienced.”