Although City emerged 2-0 victors at the Etihad Stadium to leave them trailing early Premier League leaders Manchester United on goal difference by the end of the day, they did not claim the points without a struggle.
Indeed, David Moyes and his players were left cursing the performance of World Cup final referee Howard Webb and his officiating team, whom they felt got key decisions wrong, particularly in the build-up to Mario Balotelli's opener.
It was particularly galling for Everton because they had carried out Moyes' plans to perfection.
Jack Rodwell tailed David Silva throughout and the Toffeemen succeeded in building a big blue wall around Tim Howard's penalty area that City found it very difficult to penetrate.
"If you are part of the big four maybe you can fight fire with fire, but for the rest of us, we have to come up with a gameplan," said Everton and England defender Jagielka.
"Obviously, it didn't work. But it wasn't too bad for the majority of the game.
"When you come to City, you need that rub of the green.
"They have so many attacking options and keep the ball for such long periods, if you aren't lucky then you aren't going to win the game.
"It's as simple as that."
Like Moyes, Jagielka felt Everton got the worst of the decisions.
However, in recognising City carried almost all the attacking threat, he detected a greater sense of belief within a team Everton had beaten on their previous four meetings.
And, while the 29-year-old is not prepared to say Roberto Mancini's side will break the seven-year United-Chelsea title duopoly, Jagielka knows they will not be far away.
"A few of their players have settled down now," Jagielka said.
"You can tell they believe they should be where they are now, rather than maybe just hoping.
"They will be there or thereabouts come the end of the season.
"Whether they've got enough to pip Manchester United and Chelsea, who have the experience of nicking an away win on a cold December night despite playing badly, time will tell.
"It will also be interesting to see how they cope with the Champions League, and if that has an effect on their league form."