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Villa inflicted a ninth defeat in 12 matches on Pep Guardiola’s floundering team to strengthen their position in the top half of the table.
Jhon Duran and former City player Morgan Rogers got the goals with Phil Foden netting a last-gasp consolation for the visitors.
The win was Villa’s third on the spin at home in the Premier League and Emery claims his players had sensed their opponents lacked belief.
He said: “Our confidence was increasing and theirs was going down. The players responded on the field.
“We were starting the match trying to press strongly, in the first minute we did fantastic,” said Emery.
“In 90 minutes you have to do more things, Manchester City are a little bit under the confidence they had normally.
“The second half was different, we dominated and we scored. Through those circumstances they were feeling worse than even in the first half.”
Duran was denied by City keeper Stefan Ortega inside the opening 20 seconds before putting Villa in front with his 12th goal of the season in all competitions.
Rogers, who had earlier hit the post, then doubled the lead 20 minutes after the break and Villa were cruising to the finish before Foden netted with seconds remaining.
It was Rogers’ fifth goal of the season and he remains one of only two outfield Villa players to have started every Premier League match this season.
“He has responded very well, being consistent,” said Emery. “How he played 90 minutes, scoring goals, helping the team.
“We were building up and we needed to connect with our 10 and 8s. He was really doing a fantastic job in this situation.
“One of the qualities he showed, he did a fantastic drive, he broke the lines and we could get through, through him.”