Although the team will be making its first appearance in the finals since 2002, many pundits see Marc Wilmots' squad, which is brimming with talented youngsters, as one of the title contenders, not least because the side has been drawn in Group H alongside Algeria, Russia and South Korea.
However, Hazard believes it would just be a great achievement for Belgium to make it to the quarterfinals.
"Everybody says that we have a great generation and that we can achieve something big. But we just try to stay down to earth," the Chelsea attacker told reporters.
"We know we're a young team, a very good team yes, but a young team. We'll try to go through the first stage and if we can go to the quarters or the semis, it would be exceptional for our generation."
The Belgians take on Cote d'Ivoire on Wednesday as part of their preparation for this summer's showpiece and Hazard is looking forward to playing against former Chelsea star Didier Drogba.
"Drogba is a legend at Chelsea and he'll stay a legend," the 23-year-old enthused. "I was happy to watch him play on TV and now I'm happy to play against him."
Hazard and Drogba previously met on the pitch in last week's Champions League encounter between Chelsea and Galatasaray.