The England international admits that he was sceptical before meeting sports psychiatrist Peters, who has worked with the club since 2012, but he believes that his influence has been clear.
"The way he works is brilliant," Sterling told the official Liverpool FC magazine.
"At first I thought it wasn't for me. On the outside you might think it's complicated, but all the messages are very straightforward.
"He understands the players and the emotional side of the game. What he says really helps you."
Peters will work with the England squad at this summer's World Cup.