City missed their first opportunity to seal the crown as Chelsea came from behind to win 2-1 at the Etihad Stadium.
Sterling had put the leaders on course for the victory that would have secured a third title in four years but Sergio Aguero then fluffed a penalty before half-time.
Chelsea hit back after the break with Hakim Ziyech levelling and Marcos Alonso grabbing a winner in injury time.
England forward Sterling said: "We were in a great position. It was a day to get it over the line and sadly we couldn't.
"We had chances to finish the game off, we didn't and got punished.
"It is frustrating one to take but we have still got three games to go and hopefully we'll make it right in the next couple of weeks."
Aguero's missed penalty was the main talking point after the game. The Argentinian attempted to beat Edouard Mendy with a Panenka-style kick but the Chelsea keeper was not fooled and stood up to make a comfortable save with one hand.
Aguero, City's record goalscorer, later said sorry on Twitter.
"I would like to apologise to my teammates, staff and supporters for missing the penalty," the striker wrote on Twitter. "It was a bad decision and I take full responsibility."
The error proved a lifeline for Chelsea, who were much stronger in the second period.
"If the penalty goes in in the first half the game is over and done with," Sterling said. "It kept them in the game and they won it late on."
It was not the only penalty drama, however, with Sterling believing he was denied a spot-kick shortly before Alonso's winner after falling under a challenge from Kurt Zouma.
"For me I couldn't get a shot off," Sterling said. "I don't know how it is not a penalty or has not been reviewed properly."
The sides will meet again in the Champions League final in three weeks' time but, after manager Pep Guardiola made nine changes, City have given little of their hand away.
Sterling said: "The final in the Champions League will be a completely different game and I'm sure we'll get over the line in that one."
Chelsea have other matters to think about before that final. The win lifted them to third and strengthened their grip on a qualification place for next season's Champions League but that job is not yet done. They also have the FA Cup final next weekend.
Alonso said: "I think first we need to secure the top-four position. This was a big step but there are still three games to go and we need to keep thinking game by game, and try to work hard to keep getting the results."
Alonso netted the winner as he just got ahead of Callum Hudson-Odoi to turn in a Timo Werner cross.
He said: "I think he kicked my foot but at the end of the day it's the goal that counts, whoever scores it, and the three points for us. That's the most important thing. We've got to keep going and it was important to win."