The champions lost ground in the title race as they were held to a 1-1 draw by the battling Toffees in a feisty final match of 2022 at the Etihad Stadium.
The result left them seven points behind leaders Arsenal but, with an intense schedule in the coming weeks, Akanji does not want to dwell on one frustrating afternoon.
The Switzerland defender said: "We tried to score a winning goal. We had some opportunities but they didn't want to go in. We tried until the last seconds but it was one of those games.
"We gave the opponent one opportunity - I think it was their only shot on target - and they scored.
"But we got one point. We try to keep putting pressure on Arsenal.
"It is still a long season. We have still got so many games to play. It is a busy January we've got now, and we'll try to win all of our next games and we'll see how it's going to be."
City face back-to-back games against Chelsea in the Premier League and FA Cup on Thursday and Sunday respectively.
They also have a Manchester derby, two games against Tottenham and a Carabao Cup quarter-final at Southampton - with the prospect of more fixtures in that competition - in the next month, as well as a home clash with Wolves.
Saturday's setback came after the prolific Erling Haaland had put City ahead with his 27th goal of the season in the first half.
Demarai Gray levelled with a stunning strike just after the hour and, from then on, Everton's plan to continually break up play and disrupt City's flow while defending doggedly worked perfectly for them.
City's rhythm also never recovered from a long stoppage while one of the assistant referees had his headset repaired.
"It wasn't easy," said Akanji. "We had to stop for five or six minutes because the microphone was broken, then after every duel an Everton player lay on the floor for, like, two minutes.
"Eleven minutes (added time) in the end wasn't enough because we had to wait for such a long time but we still played good."
For Everton, a point represented an excellent result, ending a run of three successive defeats that plunged them towards the relegation zone and piled pressure on manager Frank Lampard.
Defender Ben Godfrey, who was involved in a running battle with Haaland, felt the performance set a new standard for the team.
He said: "I think we showed our character. We've always had team spirit but the Boxing Day result was upsetting.
"It highlights our character to have such a disappointing result then come to a place like City and get a result.
"That's the standard. It feels good to get a point."