Carragher said: "Why would anybody want to walk away from a club that had reached a European Cup final? These are good times at Liverpool and the result against Juventus shows the club are going places.
"I'm sure Stevie will have been delighted back home. We are desperate for him to stay but it is his decision. If we get to the final of the Champions League though it must have an influence," he added.
And Carra was keen to add his respect to the tactical mastermind of Rafa Benitez.
"Really the success is down to the manager's tactics. He has played some different formations in Europe and always comes up trumps and he was up against a manager like Fabio Capello," he said.
"He changed our formation and got the right result so the credit should go to the manager for the way he outwitted their man. The boss didn't just want us to sit back and defend, because that invites pressure. He wants us to defend higher up the pitch because in simple terms they have to play further away from our goal."
And Carra said the spirit and determination of the team showed just what this team can do.
"We were down to the bare bones," he said, "but that makes you come together more in situations like this. Players came in and did superbly, like Anthony Le Tallec for example late on. Earlier in the season he couldn't even get a game for St Etienne on loan but now he's playing in a Champions League quarter-final so you can see how people can rise to the occasion."