Leon Bailey's deflected strike in the 74th minute gave Villa a club record-equalling 14th consecutive home victory.
City boss Pep Guardiola believes Villa could "definitely" be among the teams in the title fight at the end of the season.
Emery's men are just four points behind leaders Arsenal, who visit Villa Park on Saturday for a significant showdown.
But, ahead of the clash with the club that sacked him in 2019, Emery played down Villa's hopes of winning the title for the first time since 1981.
"We are not contenders. There are seven teams who are contenders more than us," Emery said.
"Now we are on game 15. We are going to play game 16 on Saturday against Arsenal and we are going to focus on it.
"We are happy to be third but to keep it is going to be very difficult."
Although Emery was keen to keep a lid on expectations among Villa fans, at the very least their superb run has carried them into contention for a top-four finish.
And even the cautious Spaniard conceded he would start to think about a title bid if Villa keep playing with their current quality and desire.
"While we are there we are going to try to keep it. If we keep progressing during the season, playing matches and winning like we are doing maybe we can be a contender but I think we need more time," he said.
"We can believe but we are not contenders. Maybe by game 30 or 32, but not yet."
Wednesday's win gave Emery his first success over Guardiola at the 14th attempt, 15 years to the day since they first came up against one another.
"Always I like to prepare matches against the best teams, the best players and the best coaches," Emery said.
"When you are playing in a high level the opponents are of a high level. But beating him for me is not something special. It is really a process I am doing as a coach."