A late goal from Stewart Downing ensured Brendan Rodgers' first competitive match as manager proved successful, while Carragher amassed his 700th appearance for the club.
"Every game for Liverpool is massive - it doesn't matter where it is - and I'm proud to have played that many games," he told the club's official website.
"It was a nice night for me on that score, but it was more important because it was the manager's first game. That's more important than me playing 700 games.
"It's a big thing for a manager in his first game, especially playing in Europe.
"It's a big thing for Liverpool, great tradition and it's great we got the victory for the manager more than anything."