Wayne Rooney's 200th Premier League goal was followed by a red card for Kyle Walker, but Everton could not hold on in the second half as Raheem Sterling equalised eight minutes from time.
Morgan Schneiderlin was then sent off for Everton, too, and Koeman acknowledged that, regardless of the circumstances, this was a good result for his side.
"I'm disappointed," he told Sky Sports. "Maybe you will take the point before the game, but we were 1-0 up at half-time, 11 against 10.
"But even with one less player on the pitch, City have that great talent. They can make it really difficult. We had problems in keeping the ball and we played the long ball too fast.
"But I thought we controlled it well — the tactical plan was outstanding in the first half. We worked really hard for a good result and one point away at City is a good result."
While Everton have made a strong start to the season, previously winning four games in all competitions without conceding after huge investment in the transfer window, Koeman is still hoping for further moves in the market if the Toffees are to kick on this term.
"We are looking for a left-footed central defender and back-up for Leighton [Baines] — without [Ramiro] Funes Mori, we don't have any back-up," he added.
"That's an option, but also a striker. Even with the talent of Dominic and Ramirez, look at other squads — they have a number of players.
"If we want to make the next step, we need a striker in as well."