The West Midlands side secured the Champions League spot on Tuesday after Tottenham suffered a 2-0 home loss to Manchester City in the Premier League. Aston Villa had won the old European Cup, the precursor to the Champions League, in 1982, but have not played in the continental competition for 41 years.
Villa are fourth in the Premier League standings with 68 points, five more than Tottenham, who sit fifth with one game to play. City are now within touching distance of an unprecedented fourth successive Premier League title.
"It's a very special day today," Emery told Villa's website. "It was our dream when we started the season to be here. To play Champions League is, after the Premier League, the best.
"You can play in the Premier League against the best teams in the world, it's very difficult. When you are playing in the Champions League you are playing against the best teams, at the same time, from other countries. And it's amazing.
"And we are always responsible about the history here, we know the history of Aston Villa is so long and so successful. Even in the Champions League, before it was the European Cup, we knew the responsibility was to try to increase our level, try to be demanding and to dream.
"I want to enjoy more and, next year, now the new challenge starts for us. To build again a team, and being strong to go and always increase our level. This is our objective."
The confirmation of their top-four finish coincided with the club's End of Season Awards Dinner at Villa Park, where captain John McGinn also spoke on the achievement.
"On behalf of all the players, it's been an amazing season," the 29-year-old Scotland international said.
"We got promoted, we got into the Premier League and were seven points behind with four games to play, we managed to stay in the league.
"We kept building and thankfully we've achieved something we haven't done for 40 years. So, on behalf of all the players and staff, we're over the moon, we're delighted."
Villa will conclude their campaign with a trip on Sunday to in-form Crystal Palace, who are 12th in the league.