Sterling was on the scoresheet as Pep Guardiola's charges moved to within three points of top-flight glory, courtesy of a commanding win that also featured goals from Gabriel Jesus and Ilkay Gundogan.
"We needed a big turnaround and from the beginning we started strong. They put us under pressure but we started well," Sterling told Sky Sports News after the match.
"[On the penalty] I remember seeing the keeper running out and I thought I'd get a touch before him and I got a penalty so I can't complain.
"In the game against Manchester United I snatched a few and didn't take my time. Today I tried to take my time and be composed."
A loss for Mauricio Pochettino's charges saw Spurs give up a 14-game unbeaten run in the league.