The Toffees delivered a disciplined defensive performance against their big-spending opponents, with Jack Rodwell handed a man-marking assignment on David Silva.
Though their massed ranks were eventually breached by substitutes Mario Balotelli and James Milner, City had struggled for three-quarters of the game.
And, with City hoping to challenge for the Premier League title, Jagielka has warned they will come up against those tactics on a regular basis.
"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 the Everton defender.
"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."
Everton had beaten City on their previous four meetings and Jagielka has detected a greater sense of belief within Roberto Mancini's current side.
"A few of their players have settled down now," added Jagielka.
"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."