The Hungarians, World Cup runners-up in 1954 with their golden generation, last featured in the Euros in 1972 when the final stages were a four-team affair.
They last played in the World Cup 30 years ago.
Hungary are expected to struggle in Group F which also includes Cristiano Ronaldo's Portugal and Iceland.
"We want to show we are not here by chance," Storck told reporters. "We have worked hard ... and we want to show we deserve to be here."
Hungary's last major tournament appearance was in the 1986 World Cup but their return to the big stage is in no way intimidating, said Storck, especially after they beat Norway twice in their qualifying playoff encounter.
"For us it is a historic game because we are again at a major tournament...although the countries have played each other more than any two other nations in Europe," the German added.
Storck conceded Hungary are the underdogs but that is a role his players are comfortable with.
"Nothing has changed," he said. "Obviously we want to play at the same level against Austria.
"But on paper when you look where these guys are playing, we know our role in this game. We are brimming with confidence and will challenge Austria."
Storck is without 27-year-old forward Gergo Lovrencsics who was hurt in training on Sunday and is likely to miss the entire competition.
"He sustained a knee injury and we don't know yet if he can remain," the German said.
Defender Tamas Kadar was also injured and is doubtful for the game with Austria.
Storck is set to pick veteran keeper Gabor Kiraly, 40, who will set a record for the oldest player in the history of the competition if he plays.
"He should set a record," the coach said. "I have known Gabor for almost 30 years, he is an outstanding player.
"We have no old or young players. We only have good players and he is still outstanding at his age."
(Reporting by Karolos Grohmann; Editing by Tony Jimenez)
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