Haaland had the chance to set the four-time defending champions on course for only their second win in 13 games when stepping up for a 53rd minute spot-kick at the Etihad Stadium.
But he was denied by Everton goalkeeper Jordan Pickford as City's woeful recent run was extended.
Pep Guardiola's team had lost nine of their last 13 games in all competitions and this draw means City picked up only their fifth point in the league since the end of October.
Bernardo Silva's deflected shot gave City the lead in the 14th minute, but Iliman Ndiaye levelled in the 36th.
The day's early result left City sixth in the EPL standings with seven games to follow, 11 points behind leaders Liverpool, having played two games more.
City boss Guardiola said: "We played really good, but we are in a period right now that this is what happens. But yeah, keep going."
He added: "Confidence will be with the results, because always is in our minds. But the performance against that team was really good, defensively, offensively. We shoot a lot in the 18-yard box, but unfortunately we could not get the result we wanted."
Haaland's missed penalty means the Norway international has only scored once in his last seven games. He headed in from the rebound, but the goal was ruled out for offside.
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