City, managed by Pep Guardiola, now sit five points behind leaders Arsenal, who are coached by Mikel Arteta. With a game in hand, the champions remain in contention, but Arsenal now firmly control their own destiny.
Despite dominating possession, City initially struggled to break down an Everton side set up by David Moyes to absorb pressure. The breakthrough came three minutes before half-time when Doku curled a superb effort into the top corner.
Everton improved markedly after the interval and equalised in the 68th minute under bizarre circumstances. A misplaced backpass from Marc Guehi caught Gianluigi Donnarumma off guard, allowing Thierno Barry to pounce. Initially ruled offside, the goal was awarded following a review.
Momentum swung further when Everton took the lead five minutes later, Jake O'Brien heading home from a James Garner corner. Barry then added a second from a Merlin Rohl assist, putting the hosts 3-1 ahead.
City responded late, with Erling Haaland pulling one back before Doku's stoppage-time equaliser - a composed finish after cutting in from the left - salvaged a point and left Everton heartbroken.
"Really good performance. We played an outstanding first half. It was so difficult with their physicality," said Guardiola.
"Second half, maybe we were not as much in control, and after we gave away the goal, they came back and made a proper English game, so aggressive in the duels.
"But in general, we made a really good performance. It is better than losing, [but of course, it is] better to win, and we played for that. It just shows what the team are."
On the title race, he added: "It depends. [The title] is not in our hands. Before that game it was, and Arsenal's as well. But now, in our hands, no.
"We have four games in the Premier League, next is Brentford, and it will be quite similar because the competitors are good, and we will see what happens. Of course, [we go into those games with belief], like we came here."
