Villa qualified for this season's Champions League after surprisingly finishing fourth in the Premier League last term.
But Emery is not satisfied with that impressive achievement and he wants to see signs Villa can maintain their top four place this season, while also competing in Europe's elite club competition.
Villa started their top-flight campaign with a 2-1 win at West Ham last weekend, but Emery sees Saturday's home game against title contenders Arsenal as the acid test of his team's mettle.
"The last history of Aston Villa is progressively getting better, but five years ago they were in the Championship," Emery told reporters on Friday.
"With the new project, with the history, with the new way we want to create here, it's about trying to be contenders and be consistent. We have to try to be progressively stronger, getting in the top four like last year.
"I don't want to waste time here myself as a coach, progressing as a coach, and I want the same mentality from the players."
Villa are back in the Champions League for the first time since 1982-83, continuing their revival since former Villarreal boss Emery took charge in October 2022.
Yet Emery won't let his players rest on their laurels, saying: "To achieve the objectives we are facing, dreaming is very difficult, but I want to dream and work hard to get it.
"At the moment we are in a good way but there's still a lot of work to do to continue being consistent like I want."
When Villa last faced Arsenal in the closing weeks of last season, late goals from Ollie Watkins and Leon Bailey earned a win that damaged the Gunners' hopes of winning a first league title since 2004.
Despite that victory, Emery is under no illusions about the threat posed by an Arsenal side who finished second in the last two seasons and started their campaign with a 2-0 win over Wolves.
"They are one of the favourite teams this year to win the league. It's a big challenge for us," he said. "They are favourites against us tomorrow."
