Gerrard reached the landmark in their draw with Newcastle United on Sunday.
"When I was a young boy, I never dreamed I was going to make that many. It was all about pulling that red shirt on and making one appearance for the club and then the dream was made. So to clock up 600 games is a magnificent achievement for me and my family and everyone is really proud," he told liverpoolfc.com.
"When I first started watching Liverpool on the terraces, John Barnes was the main man in the team. He was very exciting and one of my favourite players to watch."