The Spaniard took charge of his first competitive game for the Gunners on Sunday against the defending champions and found his side lacking as they suffered a 2-0 defeat.
But the former Paris Saint-Germain boss, who took over from the long-serving Arsene Wenger in the summer, drew positives from the experience.
“We were improving during the 90 minutes like I think we need for next week and the next match,” he insisted.
“We need to continue to work tactically with defensive options to shorten the difference between Manchester City and ourselves.
“Manchester City demanded our best performance and we saw that we have to continue working. But I’m happy with the players because they ran and they fought.”
The Gunners tried to impose themselves with a positive pressing game in the midfield but they were punished for their defensive lapses.
“This 90 minutes is how I want to do the process of improving our team,” Emery said. “We finished it with the spirit I want. The team ran, they tried and they pushed.”
A tricky start to life in the Premier League for Emery continues next week, when his side go to Stamford Bridge to face Chelsea.
Fixtures against West Ham and Cardiff are also forthcoming before the first international break of the season at the beginning of September.