Liverpool were put to the sword by Barcelona on Tuesday night, with Suarez scoring against his old side.
The Uruguay international opened the scoring in the first half last night before a Lionel Messi brace ensured the Catalan giants take a good lead to Merseyside next week.
Suarez outraged Liverpool fans, however, by celebrating his goal with gusto.
Players often opt for a more respectful approach but the Uruguay international could not contain himself at the Nou Camp.
And Carragher, who played alongside Suarez at Liverpool, believes his former team-mate will get a colder reception at Anfield as a result of his antics.
“I don’t think it will be as warm as he would have hoped,” Carragher told Viasport.
“He was Luis Suarez. You love him when he is in your team and you hate him when he plays for the opposition.
“It was the first time he was in the opposition and I don’t think Liverpool fans will have liked him.
“He plays on the edge, very street-wise.
“A great first goal for him but I don’t think it will be the hero homecoming he will be hoping for.”
Suarez had hinted before the game that he would celebrate any goal against Liverpool.
“In the build-up to the game it’s nice to talk about how massively grateful I am to Liverpool for all they gave me,” he said.
“But, you know me, once I’m on the pitch there will be no friendships, no companions, no thought for all the lovely moments.
“I’ll defend the colours of Barcelona with all the pride in the world.”
Suarez had three-and-a-half successful years at Liverpool earlier in his career.
The Uruguay international won the golden boot in his final campaign at the club with 31 Premier League goals.
His Reds team-mate Daniel Sturridge hit 22.
And Yaya Toure bagged an impressive 20, three more than Sergio Aguero, Wilfried Bony and Wayne Rooney.