Brendan Rodgers revealed on Sunday that he was ready to present a new contract to his inspirational skipper.
Following those comments, Gerrard scored the winning goal to secure three points for Liverpool at Villa Park — and executed a brilliant goal-line clearance to deny Christian Benteke.
“I’m sure Stevie will sign a contract and finish his career at Liverpool the way I’ve done,” Carragher told reporters. “There is no doubt about that. I’m sure he’ll sit down and sort it out in the next couple of months.
“Steve will be finishing his career at Liverpool. He is ‘captain fantastic’ every week.
“It’s not just against Villa. He’s been doing it for years, scoring at one end, saving at the other.”
Liverpool came from behind to win a Barclays Premier League game for the first time this season, with Jordan Henderson cancelling out Benteke’s smashed opener before Gerrard converted from the penalty spot.
“It is something that has been questioned about us over the last few years, going behind in games and coming back,” Carragher added. “Following on from the defeat at Southampton, we spoke beforehand about putting on a performance.
“Winning that game now makes Southampton look like a blip because we were on a good run.
“But I don’t really look too far ahead and to be honest if you asked most of the lads, they wouldn’t even know what position would get us into Europe. Sometimes it is fifth spot, sometimes sixth, seventh. We’ll just try and carry on and win games and see where it takes us.”