Kevin de Bruyne, Riyad Mahrez and Ilkay Gündoğan scored in the first 25 minutes to put City in a commanding position, before Sterling made in four with a superb penalty into the top corner, meaning he has scored in three successive league matches.
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The visitors mounted a comeback in after the interval, scoring thrice in quick succession, before Aymeric Laporte calmed the nerves, with Sterling adding the knockout blow with three minutes remaining in an action-packed Boxing Day clash.
The Englishman, who has five goals so far in December, was pleased to keep up his scoring form.
"I’m just happy being amongst the team, keep helping, keep chipping away, keep smiling and keep enjoying my football," he said.
"You’ve always got to be alive in there, got to anticipate the ball in there and I did just that today.
"It was a good game, but it was a bit disappointing to concede them goals but then on the plus side we kept going and finished the job.
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Despite scoring the six goals, Sterling admitted the disappointment at conceding three goals to the Foxes, who seemed down and out at half-time.
"We played some really good stuff, created chances and scored good goals but it’s a game we have to finish off and not concede them goals," he admitted.
"It’s one we’re all disappointed in. It’s one he [Pep Guardiola] tried to warn us on.
It’s as simple as we weren’t aggressive enough, we weren’t winning our duels to stop them counter attacking but it’s one we will look at and try to fix."