Billy Joel -- BOTCHES 'WE DIDN'T START THE FIRE' ... 'One of My Worst Songs Ever'

Billy Joel HATES "We Didn't Start the Fire" ... at least he sure made it seem that way during a concert in Toronto, when he screwed up the lyrics and then RIPPED the song apart.

The Piano Man was performing at the Air Canada Centre on March 9 when he tripped up over the lyrics right around the time he was supposed to sing about Rosenberg's H-Bomb.

That's when he stopped the band dead in their tracks ... and went off -- saying, "All you gotta do is f**k up one word in that song and it's a train wreck."

On the video, unearthed by RollingStone.com, Joel continued to gripe, "It's the same thing verse after verse ... Just the words change. It's one of the worst melodies I ever wrote."