Carragher played his 737th and final game for Liverpool as they ended the season on a winning note thanks to Philippe Coutinho's superb first-half goal.
The 35-year-old was given a rousing reception by the home fans before and after the game, and Carragher was delighted to bow out with three points.
"It was very emotional, especially for my friends and family in the stands who have been there to watch me all the time, but that's come to an end now unfortunately," said Carragher.
"I think the club is in good hands, we've had a good run in the second half of the season and hopefully can go from strength to strength.
"I wanted to say thank you to the supporters as that was important. It was a game we wanted to win and it was nice for my children to be involved.
"There wouldn't have been anything worse than going out with a defeat today or a poor performance that would have nagged away at me so it was just nice to keep a clean sheet and win the game."
Carragher almost marked his final game with a stunning strike in the second half which came back off the post and the defender admitted it would have been a great way to finish his career.
"I can't believe it never went in," noted Carragher. "I scored on my debut fortunately 15, 16 years ago and it would have been nice to finish that way but it wasn't to be."