Despite the loss, Kompany felt his side were the best team at the showpiece tournament in Russia.
"There was no team better than us at this world championship," the defender said, via Het Nieuwsblad.
"We had more opportunities than in 2014 against Argentina [in the quarter-finals], and had more control. We knew how we would make it difficult for this team and how we wanted to limit the risk at the back and that worked out well.
"It was a matter of details and one stood out. We respect what they have laid down."
Belgium were lively early against France, but they struggled to break down Didier Deschamps' men.
Kompany paid tribute to the winners despite their defensive approach, saying: "Everyone is obviously disappointed, it is never fun to lose a semi-final.
"We have not lost to a team that is better than us, but we have to congratulate them. They succeeded once and that was enough."
France will now contest the final on Sunday, their third showpiece in six tournaments.