The 19-year-old is expected to be included in Roy Hodgson's England squad for this summer's World Cup finals following some scintillating displays for the Reds - and has highlighted the contribution made by Peters, who will be part of the Three Lions set-up in Brazil.
"The way he (Peters) works is brilliant," Sterling told the latest edition of 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.
"We use a motto 'focus on the ball, focus on the team'. I had a meeting with him before the Manchester City game (on April 13, which Liverpool won 3-2 with Sterling scoring the opening goal).
"I thought it was going to last 20-25 minutes. So I walked in, sat down and he just said: 'focus on the ball, focus on the team'. 'Is that it?' I asked him. But it was really important."
Sterling's upturn in form has helped Liverpool climb to within touching distance of their first title in 24 years - and the former Queen's Park Rangers academy star is proud of his improvement.
He added: "You could look at the City goal as an example. I'm not trying to sound cheeky or over confident but three or four months ago I would have squared rather than take the responsibility all for myself.
"My goal was always to play for Liverpool when I first came here and maybe for a while I thought that goal was achieved because I was one of the lucky ones to do it.
"But you realise that is not enough. There always has to be the next challenge, to achieve things and win things - making your mark.
"From December time I realised I had to start stamping my personality, running with the ball, running into the box, making goals, scoring goals. Not playing with that barrier, not to be worried about making mistakes."