The Gunners were beaten 2-0 at the Emirates with Raheem Sterling and Bernardo Silva netting the goals.
It was Emery’s first competitive game as Arsenal boss after taking over from Arsene Wenger during the summer.
Arsenal fans went into Sunday’s clash with renewed optimism but the Gunners were outclassed by last season’s champions.
Emery started just one up front with Alexandre Lacazette left on the bench as Pierre-Emerick Aubameyang led the line.
Ainsley Maitland-Niles filled in at left-back though came off injured in the first half with new signing Stephan Lichtsteiner taking his place.
Fellow new recruits Sokratis and Lucas Torreira also featured though Bernd Leno was overlooked with Petr Cech starting the season as Emery’s first choice.
And with seemingly still plenty to work on, Gunners legend Martin Keown has pointed out where Emery can make changes.
“To give Arsenal more zip going forward, it might be a case of Emery playing with two strikers and trying to use the speed of Aubameyang out wide, or he could ask more from other players who are already in the team,” Keown wrote in his BBC Sport column.
“Ainsley Maitland-Niles, who started at left-back for Arsenal, is a player I admire a lot. I think he has a great future, although not necessarily in that position, and one of his strengths is how he fast he is.
“He ended up going off injured after 35 minutes against City but, when he was on the pitch, instead of taking the game to Kyle Walker down his flank it seemed like he was content just to do enough to try to contain him.
“Walker, in contrast, was being aggressive with his pace and was so keen to get forward he almost appeared to be jet-propelled.
“That is what I want to see Maitland-Niles doing too, because he is also fast enough to really hurt teams.
“But he is not the only one I would like to see some improvement from - there is an awful lot of work for Emery to do on the training pitch with all of his players.
“The fans at Emirates Stadium were desperate to get excited about anything they could on Sunday, but they did not really see enough of those sort of moments.
“This Arsenal side is a work in progress, and this is a time where their supporters need to stay with their team while they adjust to what Emery wants them to do.”
Arsenal’s start to the season doesn’t get any easier as they travel to Stamford Bridge to take on Chelsea on Saturday (5.30pm).
The Blues began their campaign with a 3-0 victory over Huddersfield on Saturday thanks to goals from N’Golo Kante, Jorginho and Pedro. SHARE THIS STORY USING ANY OF THE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇