The Spanish edged out Denmark 1-0 in their final group game to set up a mouth-watering meeting with the Lionesses.
Vilda's side only needed a draw to progress to the last eight, but a goal from Marta Cardona ensured a confidence boosting victory.
While Spain dominated proceedings, they lacked a cutting edge which could prove costly against England in the quarter-final.
Vilda said: "I think the quarter-final against England could be the toughest game in the Euros given the level England are playing at.
"They are the host nation and they have the fans behind them, but that motivates us, we are a team that likes a challenge."
Denmark head coach Lars Sondergaard expects the England-Spain clash to be a close affair, but believes the hosts can learn from his side's showing.
"If England can play past this high pressing, the pressing after you lose the ball, they have a good chance," Sondergaard said.
"They also have to be very good on the counter-attacks, but it's going to be a tight game I think.
"But England have seen two games on how to play Spain.
"They can learn from our performance, which doesn't help us, but it's going to be a tight game."
Denmark, who finished as European Championship runners-up in 2017, will head home after finishing third in their group.