Sterling broke the deadlock for England in the 75th minute and Harry Kane added a crucial second.
“We knew we need to put in a very good performance against a very good side and I thought we did that,” the Manchester City winger told BBC Sport.
“Doing it for your country is always special and it’s definitely a special moment. I wondered if it (my goal) was offside, but I was very happy it went in.
“We knew the intensity we can play at and not many teams can deal with it. The two boys in midfield, Declan and Phillips, they were class, they ate up ground. An all-round great team performance.
“We’ll take it game by game. We’ll see who we’re playing now. We’ll go away and recover and get focused on the next one.”