Sterling scored twice in City’s convincing 6-1 win over the hapless Saints at the Etihad Stadium on Sunday, netting his 50th goal for the club in all competitions along the way.
Wesley Hoedt's own goal, Sergio Aguero, David Silva and Leroy Sane completed the scoring for Pep Guardiola’s side, who went two points clear at the top of the table after Liverpool could only draw with Arsenal on Saturday.
"It was a good day's work from the team. The boys came out well. You can get complacent at home but started well and carried on throughout the game,” Sterling told Match of the Day.
"These are the games we need to capitalise on. The top teams drop points, we need to win. Big week this week. We go again in the Champions League.
"I thought it was a great team performance. Not just with the ball. We were brilliant at times today.”
After scoring either side of half-time, Sterling passed up the opportunity of a hat-trick in the closing stages by choosing instead to set-up Sane for City's sixth goal.
The former Liverpool forward says that’s a sign of the spirit and togetherness in the City squad as they look to retain their title.
"Leroy is always a man who looks up for me,” Sterling added. “He always has his eyes open. I was on a hat-trick but I am happy to set one up for him.
"I am grateful for the position I am in, learning and trying to get better. It is great times at the moment.
"After Liverpool dropped points it was important that we won today. They are a brilliant side."
Those thoughts were echoed by Germany winger Sane, who added : "I was lucky at the end with the goals, I tried to score in the game, but the whole team was really strong today.
"You can see we're keeping going with how we play from last season, we enjoy playing together. It was important to be top today."
Man City will now turn their attentions to the Champions League and a tie against Shakhtar Donetsk on Wednesday before welcoming rivals Manchester United to the Etihad Stadium in the Premier League next weekend.