Suarez won a penalty that Charlie Adam converted before playing in Carroll to virtually seal the three points for his side before half-time.
The former Newcastle frontman hailed his team-mate's ability and also declared himself pleased with his own display as he looks to stake his place as a key member of Kenny Dalglish's starting XI.
"Suarez is fantastic to play with as you can see," Carroll told ESPN after the match.
"He creates chances for everyone and then puts them away himself when he gets them. He is fantastic to have in the team.
"It is always nice to score personally and I've missed a few games sitting on the bench so it's nice to get a chance and to put one in the back of the net.
"I think I know what I’m capable of doing when I am in the team, but I've just got to do my best. I thought I helped out the team today and we deserved the three points."
Goalscorer Adam was pleased to secure the points but thought the Liverpool performance still left room for improvement.
"I think in the first half, once you get the goal, it changes the complexion of the game," he said.
"But I thought first half we played well, second half, we never kept the ball as well as we should have, and it's something we'll have to get better at.
"To come here and get three points we're delighted with, though. At times we have been disappointed in the results that we've had this year. Last week against Norwich City we had numerous chances and we could have killed the game off but that's what happens when you play in the best league in the world.
"If you don’t score, you can get punished and we did. We've done that a couple of times this year but I thought today we started the game extremely well and probably deserved to win in the end."
The 25-year old identified Carroll as one of his side's outstanding performers but admitted he had to fight off the big striker in order to take the penalty.
"I was trying to blank him out but he had a right go at me and said he wanted to take it," laughed Adam.
"But I was just glad I stepped up and managed to get the goal and it set us on our way. The big man [Carroll]'s been unbelievable today and the finish on the second goal was terrific."
Suarez was clearly delighted after the match, tweeting to his followers: "Very happy for the victory away from home. We take a step forward in the Premier League! Let's keep working!"Lucas Leiva added: "Important three points today and also to keep the clean sheet gives us more confidence. Thanks to all the fans for your support."