Did you host it on youtube? Or directly on facebook? Uploading to vimeo and linking from there is less likely to lead to issues.
Youtube’s copyright protection system doesn’t work, it’s incredibly overzealous. I made a video using a track from their approved list, they took it down anyway, then ignored their own appeals process so I gave up on them.
The question of copyright infringement’s not a simple one but at the end of the day- you’re not passing off the music as your own, and you’re not disadvantaging the copyright owner. In fact you may be advantaging them, especially if you credit it properly- people may hear the song then investigate the band. The fact that it’s legally copyright infringement isn’t the only question that the copyright holder should be asking but, unfortunately, the system isn’t that subtle.