The 51-year-old Spaniard was speaking prior to Sunday’s home game against Manchester United, his first game in charge.
He led Arsenal between May 2018 and November 2019, and now he is entering his second stint in the Premier League.
“My dream is to win a trophy with Aston Villa,” said the ex-Villarreal boss.
“It’s my personal challenge at the beginning. My second dream, my objective will be to play in Europe.”
Emery’s only full season in charge saw Arsenal finish fifth, missing out on Champions League qualification. Emery guided Arsenal to the 2019 Europa League final, which they lost to Chelsea 4-1.
After only 18 months in charge, he was fired in November 2019 as a result of a string of disappointing performances.
The Spaniard has a successful track record in European competition. Between 2014 and 2016, he led Sevilla to three consecutive Europa League titles.
Following his departure from Arsenal, he assisted La Liga team Villareal in winning their first European championship, defeating Manchester United 11-10 on penalties in the 2021 Europa League final after defeating the Gunners in the last four.
He now hopes to use that experience to bring success to Aston Villa, who have not won a trophy since lifting the League Cup in 1996.
“I have played against a lot of teams in the world,” said Emery, who was appointed as Villa manager following the sacking of Steven Gerrard. “English teams, for me, are a big challenge to play against them. The Premier League now is maybe the first league in the world.
“Each team gave us some experiences playing against them when I was at Arsenal. I learned playing in Europe for 15 years in a row, against lot of English teams.
“I am happy to be here. I decided to come here because it’s a great project and our ambition is going to be together, step-by-step.
“I want to improve here, to help with my experiences.”
His first focus, however, is on back-to-back games against Manchester United. After hosting Erik ten Hag’s side for his first Premier League game as Villa manager on Sunday, they then travel to Old Trafford for a third-round EFL Cup tie on Thursday.
“We have to start thinking only the next match because we are not in a good position in table,” said Emery, with Villa 16th in the Premier League, one point above the relegation zone after losing three of their last four matches and winning just three of 13 games all season.
“Each match is going to give us a lot of information about the players. I want to test them individually and collectively. The next match is my only focus.”