Andy Webster’s 79th-minute own goal handed Liverpool a slender 1-0 lead to take back to Anfield, and in particular, Sterling sparkled for Brendan Rodgers’ side.
The 17-year-old’s pace and trickery provided a constant threat on the left wing, and Carragher is confident Sterling will break into the Liverpool first-team on a more frequent basis this season.
“I think the way the manager wants to play is with wide men and that suits Raheem down to the ground,” Carragher told ITV.
“He’s come in and he’s done very well. He’s only a 17-year-old and it looks like he’s got a big future at the club.
“This club’s got a great tradition of bringing young players through and we brought another one on tonight in Adam Morgan. He’s also come through the Academy and Raheem’s got a few starts now this season.”
Carragher admitted the new manager and squad are still coming to terms with the changes at the club following Kenny Dalglish’s sacking in May.
The 33-year-old centre-half is hoping victory at Hearts will provide Liverpool with a timely boost ahead of Manchester City’s trip to Anfield on Sunday.
“Now we can all look forward to Manchester City, which will be a massive game. A new manager has come in and he’s finding his feet. We’re all getting used to each other,” he added.
“Getting the side to where we want it to be doesn’t have to be a slow process. The pre-season has gone really well.
“Obviously we got a bit of a bump at West Brom and we didn’t want that result. So it was nice to come here and get the result after a difficult game.”
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