What the Court held was that they could not be citizens of the United States, and thus that they could not sue in federal court under federal courts’ diversity-of-citizenship jurisdiction. The Court didn’t hold that they couldn’t be “American” citizens, as that wasn’t the issue in the suit; several states continued to recognize particular blacks as state citizens after the decision.
I don’t like the term “African-American” in relation to slaves, because slavery denied them American-ness. Thomas Jefferson referred to slaves as “a captive nation,” and that’s how the law treated them. This was changed by the Citizenship Clause of the 14th Amendment.