The centre-back on Thursday night played the full 90 minutes as a 1-0 win was secured over FC Gomel in Belarus in the first leg of their Europa League third qualifying round tie.
But Carragher, second in Liverpool’s all-time list of appearances behind Ian Callaghan (857), was not interested in another personal landmark and instead wanted to focus on Rodgers.
The new Anfield manager only arrived earlier this summer from Swansea City and so, amid pre-season friendlies, it was his first meaningful fixture at his new club.
And Carragher told Liverpool’s official website: “It was a nice night for me on that score (700 games) but it was more important, because it was the manager’s first game.
“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. As I said, his first game was more important than my 700.”
Liverpool failed to impress again Belarusian top-flight side Gomel, who are midway through their season, but Carragher thought that was due to the different stages of preparation.
“We’re pleased with the victory,” he said. “It was a tough game, as European away games always are.
“They’re in the middle of a season and I think you could see that in the fitness levels – they were much better at times than us.”