Villa went into the Group E fixture knowing that a two-goal victory would guarantee top spot, yet Emery opted to make five changes to the team that had previously defeated Tottenham Hotspur.
However, despite facing pressure from the impressive Polish outfit, the Premier League outfit were able to post a 2-1 victory in the West Midlands on Thursday night.
Moussa Diaby put Villa into a fourth-minute lead before Ernest Muci got Warsaw back on level terms, only for the returning Alex Moreno to convert from close range in the second half after a cleverly-worked free kick.
A point away at Zrinjski Mostar will be enough for Villa to confirm first place, while Warsaw need to avoid defeat in their final fixture against AZ Alkmaar to join Villa in the knockout stages.
Speaking to TNT Sports, Emery did not have a bad word to say about his players, who performed even without the likes of Emiliano Martinez or Ollie Watkins in the team.
The Spaniard said: "I'm very happy. Our reaction was fantastic. We are not 100% first in the group but I think normally we are going to win. We are settling with the players in this competition. At Villa Park with the supporters, we are playing very good.
"They were very focussed, very motivated. It was very tight to qualify for the next round. They needed a draw or a win. For us, it was important to try to win.
"We were consistent in our game plan. The second half, our control was better than the first half. We controlled it better. They had one chance off the cross bar."
Villa now face a run of three Premier League matches in quick succession before their next European encounter, starting with a trip to Bournemouth this weekend.
Home contests then follow against Manchester City and Arsenal respectively, clubs who sit above Villa in the standings but with Emery's side just two points off top spot.