Carroll joined the Reds in a £35million deal from Newcastle United on the final day of the January transfer window.
“I have had the pre-season which I needed and it has helped me get over all the niggles and injuries that I have had,” said the 22-year-old.
“I was injured a long time, so it was nice to play a few games and get my fitness up, as well as getting a few goals.
“I’m just looking forward to the rest of the season and keeping myself fit.
“Now it is a case of pushing forward. I have got to show what I can do.
“It is a big stage and I love playing for this club.
“Now I have got to do what I did to get myself here (score goals) and I am out to prove that I can do it here.”
“Kenny is a great manager and it is great to know that he has given me all his backing,” the England striker added, when asked baout the influence of Liverpool boss Kenny Dalglish.
“I have just got to give it all back to him, really.
“In training he is giving me little pointers here, there and everywhere.
“Obviously I need to listen to him and put them into my game.
“It is nice to know that he has got faith in him and it is a big help.”