Sterling opened the scoring in the fourth minute against Chelsea, who had handed City their first league defeat of the season in the reverse fixture in December.
"It was just a win and another three points. The most important thing is to get three points," Sterling told City's website.
"It was a terrific performance from the team, the manager set us up and got us ready for the game."
Sergio Aguero scored his third hat-trick of the season to equal Alan Shearer's record of 11 in the Premier League, and Sterling said he was a player City should "cherish".
"Sergio is a player we depend on," Sterling said of the Argentine, who moved to the top of the league's goal scoring charts with 17. "You saw with his first strike putting the ball in the top corner, you have to cherish players like that."
Chelsea manager Maurizio Sarri did not shake hands with Guardiola after the match, walking straight down the tunnel instead, but both managers sought to play down the incident.
"I didn't see him at that moment," Sarri told reporters. "I will see him afterwards, it was by chance."
Guardiola was keen to give his opposite number the benefit of the doubt, stressing that the two managers shared a "good relationship".
Chelsea and City meet later this month in the League Cup final at Wembley on Feb. 24.
(Reporting by Rohith Nair in Bengaluru; Editing by Peter Rutherford)
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