Crespo played only two seasons in the U.S. Negro Leagues, with the New York Cubans in 1940 and once again in 1946. The remainder of Crespo's summers were played in Mexico while he made numerous winter ball trips to his native Cuba. Alejandro compiled a lifetime batting average of .277 playing primarily for Cienfuegos in Cuba. Crespo was also a consistent .300+ hitter during his time in the Mexican League.