Luka Modric (Getty Images)
But Croatia made a similarly impressive opening at Euro 2016, beating Spain to finish top of their group, only to tumble out to Portugal.
"It's all great for the history books in Croatia but if we don't win against Denmark, when someone asks you what you did, what can you say? Nothing," Dalic said on Wednesday.
"Our first goal for this World Cup was to pass the group stage but that doesn't really satisfy myself or the team. We have Denmark against us now and that's the moment of truth."
Denmark held France to a goalless draw on Tuesday to go through as runners-up in Group C and their key threat in Nizhny Novgorod will be star midfielder Christian Eriksen.
Eriksen provided the assist for Yussuf Poulsen's winner against Peru and then opened the scoring with a superb strike in their draw against Australia.
"He is a really key player for Denmark," Dalic said. "But we can't really pay special attention just to him. We played similarly against Lionel Messi and Argentina.
"What is important is the whole team defends together, not just as individuals or the midfield player in his area. The whole team has to do it together."