Pep Guardiola’s team, leading from Danilo’s first half goal, looked well in control but Sterling’s blunder 20 minutes from time offered a lifeline and renewed belief to the home side.
And eight minutes from time, Matt Lowton’s deep cross from the right allowed Johann Berg Gudmundsson to ghost past the City backline and score with a left-foot volley from six yards.
“Of course we are frustrated in terms of the result but the performance was outstanding against a Burnley side who are the most British of teams in terms of long balls and the way they play,” said Guardiola.
“But football is about goals. We needed to score the second, third and fourth when we had the chance. When you arrive in the last 15 minutes at Burnley 1-0, this is what can happen.”
It is just the fourth time City have dropped points in the Premier League this season, but they still enjoy a commanding 16-point lead over Manchester United, who host Huddersfield later on Saturday.
A draw extends Burnley’s winless run to nine league games, but the Clarets boss Sean Dyche was delighted with his side’s reaction.
“We had to dig in and do the ugly stuff. Then the confidence started to build. We started putting quality into their box, and in the end it was a fantastic ball and a fantastic goal,” said Dyche.
Burnley were made to pay for switching off midway through the first-half when a quickly-taken Kevin De Bruyne corner found Bernardo Silva who, in turn, moved the ball on to Danilo, who had been left in far too much space outside the Burnley area.
The full-back carried the ball to the edge of the area before curling an unstoppable 20-yard, right-foot shot into the far corner.
The lead was just about merited for a City side that came to Turf Moor without seven injured first team players and with Guardiola naming just six substitutes.
– Small bench –
The City manager claimed he had not wanted to deny youngsters playing in a Friday night elite development squad fixture in order just to sit on the first-team bench.
But Guardiola’s decision was also interpreted as a gesture in response to his recent complaints that his players are not receiving enough protection from referees, leading to a long injury list at the Etihad, as well as City’s failure to land Riyad Mahrez from Leicester before Wednesday’s transfer deadline.
Despite their absentees, City were still dominant as Sterling blasted over from six yards out after good build-up play by Aguero after the break.
The chances kept coming with Danilo close to another goal from the edge of the area, denied only by Pope’s fingertip save.
Those misses might have proved costly when a Vincent Kompany error gifted the ball to Ashley Barnes and Burnley worked an opening for Aaron Lennon whose blistering shot which Ederson brilliantly tipped onto the bar.
Yet City’s run of squandered openings was about to grow, with the worst of the lot, when Sterling missed an open net from two yards as he steered Kyle Walker’s cross the wrong side of the post.
Moments later, the England forward was replaced by Guardiola and watched on in horror as City were pegged back.
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