The former talismanic centre-back, who now works as one of Sky Sports' main football pundits, believes Sturridge can flourish at Anfield with the controversial Uruguayan international now off the scene.
Carragher: The quotes
Speaking exclusively to the Anfield Wrap - and brought to our attention by the Mirror - Carragher is excited to see what Sturridge, who scored 24 goals for the Reds last season, can achieve without Suarez breathing down his neck.
“I don’t think [Sturridge] gets enough credit, I’ve mentioned it before," Carragher said. “He’s not Suarez, we know that. I remember times last season when I was in the Main Stand. In the Everton game he and Suarez were going hammer and tongs at each other, they were still arguing at the halfway line and the manager brought Sturridge off.
"I’d have done the other one.
“I felt at times that Suarez bullied him a little bit. I know with strikers there’s sometimes a little bit of a jealousy thing there, if someone’s scoring.
“I felt for him at times. I think he got the rough end of the stick at times with him and Suarez.
“I’m not saying they never got on, but they both wanted to be the main man scoring. Now there’s no doubt he’s the man."
Sturridge tipped to become Premier League's best
Carragher added that he has no doubt Sturridge can now go on to become one of the best strikers in Europe - and the Premier League's top marksman - because he possesses all of the required attributes.
“Look at his record: I think I’m right in saying he’s got more goals after 50 games than any Liverpool player ever," the 36-year-old continued. "If you look at the strikers Liverpool have had that’s an unbelievable achievement… He could be the best striker in the league.
“Think of the ability he’s got to get goals: He’s got class, he’s got pace, he scores all sorts of different goals, he’s cool when he’s going through on goal, he’s England’s main striker now and he could be one of the best in Europe.”
Watch: SAS - Sturridge and Suarez
Is Carragher right?
Certainly, there were times last season when Suarez and Sturridge had their on-field disagreements - but, on the whole, the pair appeared to have struck up a good working relationship.
Liverpool excelled with the pair of them on the pitch at the same time and went agonisingly close to winning their first league title since 1990, only to be pipped in the final weeks of the campaign by Manchester City.
With Suarez now at Barcelona, Sturridge is currently priced at around 5/1 - third favourite behind Sergio Aguero and Robin van Persie - to win next season's Premier League Golden Boot award.
But will Liverpool be as ruthless without Suarez who, despite his controversial antics, is one of the most talented players ever to ply their trade in the Premier League?
Sturridge will be flanked by the likes of Raheem Sterling and Philippe Coutinho, plus new signings Lazar Markovic and Adam Lallana. Divock Origi will also arrive from Lille.
Rickie Lambert, an out-and-out striker has arrived to ease the goalscoring burden on Sturridge, but France international Loic Remy failed his medical.
This means the emphasis will be firmly on Sturridge's shoulders to fire Liverpool as close as possible to the Premier League title - and as far as possible in the Champions League.