The Ajax coach and former Oranje international says Bert van Marwijk's men must win their opening group game against the Danes or face coming under huge pressure
The 2010 World Cup finalists face the Danes in Kharkiv on Saturday in Group B, which also contains Germany and Portugal and has been dubbed as the tournament's 'group of death'.
Speaking at the opening of a fenced football pitch in Krakow for the Johan Cruyff Foundation, which was also attended by the Netherlands squad, De Boer issued a warning to Bert van Marwijk's men.
"When you see the quality of the other teams in our group see the stars they have, you cannot deny there is a lot of quality," he told reporters.
"Therefore, they must win the first game against Denmark because then you will get a good atmosphere in the group.
"If you lose, the pressure is immense and that can become fatal."
The opening ceremony was attended by Frank's brother, Ronald, a former Netherlands international himself, and he also gave his thoughts on the Oranje's chances.
"Spain are the favourites to win the tournament," he said.
"But we also have the experience of the World Cup finals.
"Since then much has changed in the style of play and players, but the quality of the players there have come from the highest level."