Suarez was Arsenal’s sole signing of the January transfer window, on loan from Barcelona.
And after just a couple days of training, Suarez was given his first taste of Premier League football when he came off the bench against City.
But it was a rather underwhelming Arsenal debut from the Spanish midfielder, who looked lightweight in physical duels.
Arsenal visit Huddersfield this week needing a win to keep up with top-four rivals Manchester United and Chelsea.
And in his pre-match press conference, Emery called on Suarez to improve.
“His adaptation to us and also on Sunday in 25 minutes, in the first days with us, is not with good performance,” Emery said.
“This week he worked Monday alone here with our coaches and also yesterday and today he’s working with a different adaptation, better than last week.
“I hope he’s continuing to improve every day.
“Then he can show in the next matches how he can help us, better than in the first match against Manchester City.”
Huddersfield have lost 11 of their last 12 League games and are stranded at the bottom-of-the-table.
But Emery says his side must remain wary of the Terriers.
“It will be difficult. Each match is difficult and they are going to play for the possibility of continuing in the Premier League,” he said.
“Their last result was not good but with their new coach, I’m sure on Saturday they’ll play with big ambition and performance.
“They have good players, good organisation. They push a lot. I know it’s difficult.
“Away each match is a new challenge but it’s also a very big opportunity to take the three points and continue in our way better than we’re doing now away.”