An early goal by Raheem Sterling and a goal in the second half by Bernardo Silva proved to be enough in a comfortable afternoon for the champions.
The contest was the first game of the Gunners Premier League without Arsene Wenger for 22 seasons and Emery's first competitive since taking over.
While the fans expected an easier start to the campaign, some said it could be the best time to play against Pep Guardiola's men.
Many of the members of his team had just begun to train after having had a prolonged vacation due to the World Cup.
"The first half did not play as we wanted"
But in the end it was not like that and Emery was honest in his analysis of the game.
"The result was 2-0, but I think that in the field of play in the 90 minutes we were improving," said the Spaniard later.
"In the first half we did not play as we wanted, we talked at halftime about taking on more responsibility for the second half, to do a little more.
"We wanted to build with the ball and break their lines, I think in the second half we play more as we want."
Emery gave debuts to two new signings, including Matteo Guendouzi, 19, a surprise Lorient signing of £ 7m in the summer.
And it was Guendouzi who took the blame for his Arsenal teammates after Sterling bagged the first goal.
On the teenager, Emery added: "It's their first match here in the Premier League.
"He has personality and quality, and if he's on the field, he's improving very fast."
Emery now has another week to work with his players before the London derby against Chelsea at Stamford Bridge next weekend.
While the new boss could not send the Arsenal fans home with a victory, he was full of admiration for his support.
"We wanted to start here with our followers," he said.
"We wanted to show our performance, but it's clear that against Manchester City we could not give them this victory, but I think we're going to feel very good here."