Guardiola regrets Man City's dropped points against Everton
Erling Haaland fired reigning champions City into a first-half lead only for Demarai Gray to equalise midway through the second period of a match featuring numerous fouls.
The game also required 11 minutes' stoppage time following repairs to an assistant referee's headset.
The result left second-placed City seven points behind Arsenal heading into 2023 after the Gunners won 4-2 at Brighton in Saturday's late clash.
City manager Guardiola, reflecting on Everton's tactics, said: "They made a fantastic goal with the first shot on target they had, so we played a real, real good game.
"Of course the result was not expected but that is football, it is not the first time it happened. We did everything to win. They played really well."
The Spaniard added: "Afterwards they broke a bit the rhythm because the referees were not ready but, in general, we did everything and unfortunately could not win."
A battling draw gave Everton a first point in four matches and left the Merseysiders, who had lost 2-1 at home to Wolves in their first post-World Cup game, two points above the relegation zone.
"I think we did limit their good chances," said Everton manager Frank Lampard.
"And in terms of our character and discipline and following through with the plan, working consistently for 100-odd minutes, understanding that's sometimes tough and you have to stick with it, I thought we did that brilliantly and we deserved a point."
Lampard, turning to Gray's "unstoppable" strike, said: "When he hits a goal like that it just shows you the talent he's got, and it got us a point."