Villa went into the Premier League fixture on Sunday with the opportunity move 11 points clear of their opponents, who are in sixth position in the standings.
With the potential of a top-five place leading to Champions League qualification, the result could prove pivotal and Villa would succumb to a late defeat.
After Rasmus Hojlund had given United an early lead, Douglas Luiz netted a deserved equaliser in the second half, only for a Scott McTominay header to earn the visitors all three points in the closing stages.
As a result, United have catapulted themselves back into contention for a place at European football's top table for 2024-25 and now sit six points adrift of Tottenham Hotspur in fourth spot.
The gap is one fewer to Villa, who have now lost three of their most recent six Premier League fixtures to drop eight points behind leaders Liverpool.
Speaking after the game, Emery was full of praise for his side's general performance, saying that 'the game plan was carried out', but accepted that his players were not clinical in the final third.
As quoted by the club's official website, the Spaniard said: "We were being successful here at home in a lot of matches, playing a lot of matches worse than we played tonight against Manchester United.
"We created chances but we weren't clinical. Their goalkeeper played a fantastic match and we lost a very good opportunity. This is the way to build our structure stronger and to try and control the game in the structure we are progressively trying to build. We did it.
"The plan before the match we were speaking about in the dressing room and the players did it. Sometimes it was goalkeeper, sometimes we weren't clinical, but we controlled the game and avoided the transitions.
"We conceded a few chances to score but they are Manchester United and they have very good players. We have to be proud of our work, proud of our supporters, and we are fifth in the league. We lost a very good opportunity today to do a bigger gap with them but we keep going."
Villa are next in action when they make the trip to West London to face Fulham on February 17. body check tags ::