Maarten Stekelenburg was in excellent form during his sides 1-1 draw with City, having saved two penalties, one from the returning Kevin de Bruyne and the other from second half substitute, Sergio Aguero.
However, it was in-form Romelu Lukaku who gave the visitors the lead after 64 minutes before Nolito equalised just eight minutes later, but it was Stekelenburg who proved to be the hero for the Toffee's who earned an excellent point.
The point keeps Everton in sixth place on 15 points, whilst City failed to extend their lead at the top of the Premier League. Pep Guardiola's men sit top with 19 points, but are only ahead of goal difference ahead of Arsenal - who closed the gap after a 3-2 win over Swansea City on Saturday.
The best Koeman has faced
Despite having previously managed the likes of Ajax, Benfica and Valencia; Koeman admitted that City were the best opponents he has ever faced. After the game, the Dutchman was quick to praise his defence.
"Maybe the goalkeeper played his best game ever today, but our defensive organisation was fantastic and so was the fighting spirit of the team," he said.
"And you need that against City, because they are the best team I have played against in my managerial career."
Guardiola's men are without a win in three games having suffered defeat at White Hart Lane against Tottenham Hotspur and a draw with Celtic in Europe. The Blues now prepare themselves for Wednesday when they travel to Spain to face Guardiola's former club Barcelona in the Champions League.
Koeman and his players make the short trip to Turf Moor next weekend as they face new boys Burnley in the league hoping to continue their form after making a positive start to the season.