The England forward bagged his eighth goal of the campaign - and the 100th of his career - with a shot that struck the underside of the crossbar, to seal the points for the champions.
“It was a really good moment, especially at 2-1 to make it 3-1- it was a really nice feeling,” said Sterling.
“I had chance earlier on and didn’t know I was onside until I dragged it wide - you just have to stay focused.
“I was running into the box, but thinking Riyad couldn’t make that pass, but it went through the defender’s leg, I took it early and I didn’t get enough on it.
“I knew another chance would come. I was waiting for an opportunity and it eventually came.
“But you have to finish chances like that off because in the Premier League you can be punished.”
Sterling said the team didn’t panic when it went to 1-1 and Everton were pushing for a second.
Keeping calm and carrying on as normal is very much the order of the day for this City team.
“We know if have setback, we stick to our game plan,” he said.
“It’s important that we don’t get caught up doing something different after conceding and just continue playing how we do, and chances will come.
“Coming here is always one of the most difficult fixtures – I’ve always said that. We had to fight.
“We knew it would be tough get over the line.
“It is still early in season, there are still 90-odd points to play for, so we continue playing our game.
“We're behind Liverpool, but the league can change very quickly so we need to stay focused and be ready.”