That Spanish came into play and needed just a draw to move into the last eight behind second-place Germany and controlled the fight before Marta Cardona sealed victory with a late header win.
Spain dominated possession but lacked penetration at the Brentford Community Stadium but Vilda is confident his side will be up to the challenge of taking on England.
“I think the quarter-final against England could be the toughest game of the Euros given the level England are playing at,” he said.
“They are the host country and they have the fans behind them but that motivates us, we are a team that likes challenges.”
Denmark head coach Lars Sondergaard expects a close encounter between England and Spain but believes the hosts can learn from his side’s performance.
“If England can survive that high pressing, the pressing after losing the ball, they have a good chance,” said Sondergaard.
“They also have to be very good on the breaks, but I think it will be a close game.
“But England saw two games how to play against Spain.
“They can learn from our performance, which doesn’t help us, but it’s going to be a close game.”
Denmark, runners-up at Euro 2017, faced a difficult task being drawn into the same group as Germany and Spain, but Sondergaard felt they did well.
“They were in tears, they weren’t that happy, they knew they should have come through, but I think they did such a good job and I think it was the best game they had,” he said.
“If we come back after losing 4-0 against Germany, then win against Finland, then play so well against Spain, then we’re definitely on the right track.
“In the death group, we were the ones who died, but we fought for our lives.”