The 23-year-old Geordie has recieved much criticism since his move to Anfield, but after scoring against Brighton last week, he wants to link up more often with his fellow forward
Rather amazingly, that win at Anfield represented the first time that Steven Gerrard, Carroll and Suarez have all started together in the same team - and Gerrard also added his name to the list of scorers.
As well as his neatly-taken finish, Carroll provided the assist for Suarez's goal with a knockdown, and he feels that their link-up play will only improve from his return from several injury problems, now that the Uruguayan's ban is over.
"I'm getting the games I want, my fitness is up there now, and I'm scoring goals - it feels good," said Carroll.
"I haven't been fit in all of the time I've been here, but training together [with Luis] has shown we can do it [as a partnership] and against Brighton we showed we can score goals up front together.
"We've been training well together so when it comes to a game it's just natural. You saw against Brighton we both got on the scoresheet, so it's coming off."
Manager Kenny Dalglish has had to turn to Carroll during Suarez's prolonged absence, with the Newcastle-born striker starting nine of the last 13 matches; but Carroll knows as well as anyone that a place in the starting line-up is far from certain.
"We've got a great team and a great squad, so the manager could put anyone in and anyone will do a job," he added.
"I've just got to work hard this week and try to get myself in the starting XI. You've always got to stay on your toes and train well to stay in your position."
Carroll will be hoping that his FA Cup exploits against Brighton will have done enough for him to keep his place alongside Suarez this weekend.
Liverpool entertain Cardiff in this year's League Cup final, and for Carroll, in particular, this weekend's clash will be even more important as he has never previously been to a Wembley final.
"I am buzzing and can't wait for it. All of the lads are the same. It's a cup final at Wembley for Liverpool, so it's great," he said.
"I came here to win medals. Getting to Wembley is great - now hopefully we can go there and get the win."
Despite Liverpool being the clear favourites though, Carroll insists that the Reds will not become complacent and take a Cardiff side, who have visited Wembley twice in the last four seasons, lightly.
"It will be a tough game. They have got to the final too and they've got there for a reason," said Carroll.
"I know they are in the league below but they're a good team, so it's going to be difficult.
"We've got to go and think we're playing against Manchester United.
"We've got to treat it as though they are the best team we'll play against."