Slavery was implicitly allowed by our Constitution. How could the 3/5ths compromise be legitimate if slavery wasn't?
Slavery may have been tacitly tolerated in the Constitution, but the 3/5ths rule you cite is an anti-slavery, not pro-slavery, provision. The slave states wanted each slave to count as 5/5ths of a person toward the census. The fact that they counted for far less is an attack on the institution of slavery, not an attack on the merit of the blacks who were enslaved.
Slaves were counted as 3/5ths of a person for the express purpose of diluting the strength of the south in the House of Representatives. Period.