A second-half header from Samuel Umtiti was all Didier Deschamps' men needed to book their spot in Sunday's final.
Hazard was Belgium's most threatening player as his team struggled to find a way through a compact France outfit.
But the star attacker claims he would prefer to play for his team and lose than be on the winning side but playing what he called an "efficient" French style.
"I prefer to lose with this Belgium than win with this France," Hazard said, via Het Nieuwsblad .
"But they do defend strongly and are very efficient. We have not found their weak point. That little moment of magic needed to score was not there.
"We have seen a fantastic Belgian team and have been eliminated by a team that was more solid than us."
The loss saw Belgium miss out on reaching a first World Cup final, but they can still better their fourth-place finish of 1986.
And Hazard said he was proud of what Roberto Martinez's team had managed in Russia despite coming up short in their quest to reach the final.
"We have shown that we have a very nice team," he said.
"We can be proud of what we have achieved. As a captain, I am happy to be part of this team."