The Gunners struck twice in the first 10 minutes at the London Stadium thanks to goals from Gabriel Jesus and Martin Odegaard.
But just seven days after squandering a 2-0 advantage in their 2-2 draw at Liverpool, the Gunners again cracked under the pressure of the title race.
It was a hammer blow for Arsenal, who sit four points clear of second-placed Manchester City but have ceded the title race momentum to Pep Guardiola's team.
"It started extremely well again. We scored two beautiful goals. After that we made a big mistake to not play with purpose to score the third and fourth," Arteta said.
"We just thought we could play around them and keep the result. That gave them hope."
City had closed within three points of the Gunners after beating Leicester 3-1 on Saturday and it is the champions who have the destiny of the title in their hands despite trailing Arsenal for much of the season.
City, who have won their last 10 matches in all competitions, have a game in hand on Arsenal.
With a home game against Arsenal looming on April 26, City know they will lift a fifth title in six seasons if they win their remaining eight matches.
By the time Arsenal travel to the Emirates Stadium they will be seven points clear of City if they beat bottom-of-the-table Southampton on Friday.
Yet that gap would still look uncomfortably small to Arsenal fans fearing their team are in the process of wasting a golden opportunity to win a first title since 2004.
While City are battle-tested in handling the tension of the title race, Arsenal's young squad look to be suffering an ill-timed attack of nerves.
"My worry is after 2-0 we made that huge mistake," Arteta added. "We didn't understand what the game required in that moment.
"We need that ruthless mindset to go and kill a team."
