After almost 20 years at the club, Carra knows an end- of-season chat with Rodgers will decide whether he stays when his contract runs out in the summer.
He said: "The manager's been great and tried to keep me involved but I want to start. I'm no different to any other player.
"Norwich was only my second start in the league this season, which is disappointing.
"But I said I wouldn't complain and I'm just trying to get more starts between now and the end of the season. I've played a lot in Europe and the cups but the Premier League is the most important thing for the club and the players.
"We all want to play in it and I'm no different. I won't lie, it's been a difficult season for me in terms of starting games."
Carragher, who has also played more European games than anyone in Anfield history, added: "I'm open-minded and I'm sure the club are. It's not about what I'm going to do. It's up to the manager and the club to make a decision about a new contract.
"We'll chat at the end of the season. It's down to them. I'm just pleased I got the nod at the weekend and hope to get a few more games now. I played in the FA Cup, missed the Manchester United game but played against Norwich."