The £35million striker has been the subject of intense speculation about his future after a tough first 12 months on Merseyside.
Having been linked with a return to former club Newcastle reports emerged that he had been offered to Manchester City in a swap deal with Carlos Tevez.
Liverpool have refused to comment on the story, insisting they never do on transfer speculation, and Carroll has stressed his head has not been turned by speculation about moves elsewhere.
"Not at all," he said when asked whether there was any point in the last year when he had regretted his move to Merseyside.
"The club has been great with me and everyone outside the club has been fantastic and I am enjoying it down here.
"Everyone has backed me and helped us along the way. I have signed a contract here and this is the team I am playing for."
Carroll has been stoutly defended by manager Kenny Dalglish ever since his shock arrival on January deadline day last year.
However, injury affected the latter half of last season and he has not yet found his form - or a regular starting spot - with just six goals in 36 appearances for his new club.
But he played a key part for both goals in Saturday's 2-1 FA Cup fourth round win over arch-rivals Manchester United at Anfield.
For Daniel Agger's header he was the main distraction for goalkeeper David de Gea, who failed to get anywhere near Steven Gerrard's corner, while his flick-on sent Dirk Kuyt through for the winner with two minutes remaining after Park Ji-Sung had equalised shortly before half-time.
"I thought I had did well and everyone else did but I've got to keep working on it and it will come," admitted Carroll.
"I am just getting into my stride now. Everyone is getting used to how I play and I am getting used to everyone else.
"Everyone is helping us as much as they can and I just need to get going.
"I thought everyone played well and we deserved the win really. Everyone put a shift in and got what we wanted out of it at the end.
"Obviously it was nice to get an assist but it doesn't really matter who sets them up or scores them really, as long as we get through like we did with everyone playing well.
"Manchester United came here and all the lads were buzzing for this game and it showed as everyone was up for it and we got the result we wanted."
Carroll's determination to do well at Anfield is matched by Kuyt, who admits he had found it tough after losing his place in the starting line-up.
"It is very difficult, I am the type of player who needs games in a row," said the Holland international.
"The more minutes I play the better I feel and I have been used to playing every game for the last 10 years of my career.
"Obviously I just want to play every game and I have to try to prove that to manager every time I play.
"It is the manager's decision and you have to respect that, especially when the manager is Kenny Dalglish."
Kuyt scored only his second goal of the season, his first coming in the Carling Cup way back on September 21 but said he had remained positive despite his struggles.
"If I am not scoring goals that is not what brings me down," added the Dutchman.
"I am the type of player who needs games in a row to feel comfortable and feel better and to be honest I am playing more now than I was at the start of the season.
"I feel stronger and for me it was just a matter of time before I scored.
"We are all humans and in life you always have ups and downs.
"Last season, after Kenny arrived (in January), I played every game and scored more than 10 goals under him.
"This season I have struggled a bit with scoring goals but if I keep playing like this I will score more goals."