The Uruguayan striker spent three-and-a-half years on Merseyside between January 2011 and the summer of 2014.
A productive spell in England delivered 82 goals in 133 appearances and a PFA Player of the Year award, with his efforts carrying the Reds close to an elusive Premier League title.
There were issues as well, though, and he eventually made a big-money move to Barca while serving a ban for biting
Suarez has gone on to flourish in Catalunya, recording another 177 goals across a trophy-laden spell, and celebrated his most recent when finding the target against Liverpool.
That strike helped Barca to a 3-0 victory in the first leg of a Champions League semi-final, with Carragher suggesting that the South American will now face a frosty reception back at Anfield.
The former Reds defender told Viasport: “I don't think it will be as warm as he would have hoped.
“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 warned Liverpool that he would be celebrating if he hit the back of the net.
While the Reds form a memorable part of his past, he is fully committed to Barcelona in the present.
He had said ahead of a heavyweight European encounter at Camp Nou: “In the
“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.”
Liverpool will be back in Suarez’s sights on Tuesday, with Barca looking to build on their three-goal advantage and book a place in the Champions League final on June 1 against either Ajax or Tottenham.