Denmark drew 0-0 with Serbia in Munich on Tuesday but qualified second in the group after the parallel England-Slovenia Group C match finished with the same scoreline.
With Denmark and Slovenia equal on points along with goals scored and assisted -- and even disciplinary records -- the Danes progressed due to having a higher European qualification ranking.
As a result, Denmark -- who reached the semi-finals of the most recent Euros -- will face hosts Germany in Dortmund on Saturday.
"Everything is possible," Vestergaard told MagentaTV after the game.
"The Germans are a strong team. We need a really strong performance and to stop Germany from showing their best form."
Along with Spain, Germany have won the Euros a record three times but were defeated in the final of the 1992 edition in Sweden by Denmark, the only time the Danes lifted the trophy.
Denmark coach Kasper Hjulmand called Germany "one of the favourites" for the tournament but said he "had a good feeling about the game".
"Playing against Germany (in Dortmund) with the Danish team, it couldn't be better. It's a great team but we're a great team as well and when we play the big nations, we always step up," said the 52-year-old.
Manchester United midfielder Christian Eriksen was named man of the match in his 133rd game for Denmark, setting the all-time appearances record.
"Being named player of the match, it's something extra," said Eriksen.
"I'm very pleased we're through to the knockouts -- that's what I hoped for."
Eriksen's low corner allowed Jonas Wind to score in the first half, but the goal was chalked off as the ball went out.
The midfielder also created an excellent chance for Vestergaard with 25 minutes remaining, but the Leicester City defender headed straight at Serbia's goalkeeper.
Serbia had a goal ruled out midway through the second half when Luka Jovic was found to be offside in the build-up.
