Douglas Luiz’s double and clinical finishes from Ollie Watkins and Leon Bailey ended Villa’s Hammers hoodoo, for their first victory over West Ham since 2015.
They returned to fifth spot, just a point adrift of the top four, with games against Luton, Nottingham Forest and Fulham coming up next.
“There are seven teams contending. We are after seven teams; Man City, Man United, Liverpool, Tottenham, Arsenal, Chelsea and Newcastle,” said Emery, with fifth potentially offering a Champions League place this term.
“Dream, always. My dream is to win the Champions League but now we are fifth and we are going to face each match trying to get a good performance.
“It’s 38 matches and we lost at Newcastle, we lost at Liverpool. They are matches we are not going to play again.
“I prefer to speak about the matches we won but I have to speak about the matches we lost. This is the balance. We have to be very demanding.
“In the table West Ham were two points behind us and the level we have now, they have as well. It was very important.
“The process is going in the right way, it’s going to be difficult. In the end we won 4-1.”
Luiz had already tested Alphonse Areola from distance before opening the scoring after half an hour, firing in from the edge of the box after good work by Nicolo Zaniolo and Watkins.
Six minutes after the break Villa were gifted a second when Lucas Paqueta sold Edson Alvarez short and he brought down Ezri Konsa for Luiz to convert from the spot.
But Jarrod Bowen grabbed a lifeline for the Hammers soon after when his shot hit Pau Torres to creep into the corner.
The visitors sensed a recovery, Matty Cash heading over Nayef Aguerd’s shot, but with 16 minutes left Watkins ended any ideas of a comeback. He latched onto John McGinn’s long ball, skipped past Kurt Zouma and lashed into the roof of the net.
There was still time for Bailey to get in on the act in the final minute, beating Areola from six yards after giving Aguerd the slip.
It was just West Ham’s third league defeat of the season, leaving manager David Moyes frustrated.
“I’m not having my teams losing four goals as soft as we did today. There were things which I can say we did quite well but I didn’t think we were hard enough to play against,” said Moyes, whose side are now ninth.
“Today wasn’t so good. More importantly nearly every ball we played around the box was the wrong decision and it led to us hardly creating enough opportunity to score.
“The lads kept on fighting and it looked like we were the team in ascendancy at 2-1 but they punished us really quickly and that took the game beyond our reach.
“Villa are probably just behind the top three or four in the Premier League and today was a challenge to see what level we were at and I thought we fell below that.
“It was a very close first half, we missed opportunities to score. We had opportunities to make chances to score and that was the bit bugging me at half-time.”