Church announced the cancellation in a message to his supporters Tuesday -- explaining he wants to watch the Tar Heels game on Saturday night so badly that he won't be able to perform at the AT&T Center in San Antonio.

Church called the move "the most selfish thing" he's ever asked of his fans in a statement to them ... but he implored them to understand because the game just means that much to him.

"I've watched Carolina and Duke battle over the year," Church said, "but to have them matchup in the Final Four for the first time in history of the NCAA Tournament is any sports enthusiast's dream."

Some fans, though, were not understanding ... as several stormed his official Facebook page to let off their frustration.

Some called him a "clown," while others said they'd boycott his concerts going forward.

To be fair to Eric, the game is being heralded as one of the biggest college basketball games ever -- and the dude does love Carolina (he's got a hit song about it!).