Cure the Blues, the undeafed favorite for the Kentucky Derby, won his 1981 debut by five lengths this afternoon. But his performance hardly supported the belief this may be the next American superhorse.

His apologists will point out that Cure the Blues stumbled badly at the start, spotting his rivals about four lenghts. That he lost a shoe in the early stages of the race. That he won with only minimal urging by his jockey. e

But trainer LeRoy Jolley did not seem to be wearing the countenance of a man who knows he is going to breeze through the Triple Crown series. There is a long road ahead.

On the basis of his brilliant record last year and his training this winter, Cure the Blues looked ready to run a fast seven-furlong race. But his time, 1:23 flat on a sloppy but quick Hialeah racing strip, was mediocre.

And the lost show on the foot that has caused him so much trouble suggests that he may be plagued by further physical difficulties this spring.

Cure the Blues' five rivals in this allowance race did not figure to give him much competition, as his 1-20 odds suggested. And they didn't. When the gate opened, the colt stumbled so badly in his first stride that jockey Jacinto Vasquez said, "I thought he'd go down." But as soon as he recovered, he accelerated along the rail and caught the fainthearted front runner, El Graca, after a quarter-mile.

Two of his rivals attempted to launch challenges on the turn, but when Vasques cracked Cure the Blues with his whip one time the colt drew away and defeated Governor Bob by five lengths. He covered the last eighth of a mile in 12 4/5 seconds.

Jolley would have preferred not to run his colt on the sloppy track, but with so little time remaining until the Derby he has little flexiblity. Cure the Blues is scheduled to run at Aqueduct in the Gotham Stakes April 5 and the Wood Memorial April 18. "If we're going to make those races, we had to run today," Jolley said.

The lack of flexibility in his schedule makes Cure the Blues' right foot a source of worry. He missed his first scheduled race this year because of that foot, and today he lost the shoe because the nails would not hold in the weakened wall of the hoof.

Cure the Blues is, of course, still unbeaten and unchallenged and, Jolley said, "He got three races of experience out of this one." But the Gotham will be more than the formality it was once expected to be. It may reveal whether Cure the Blues is indeed genuine.