The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States;
Here's a link to the decision. Point out where you think the 16th Amendment is at issue...
"(c) Even if the mandate may reasonably be characterized as a tax, it must still comply with the Direct Tax Clause, which provides: “No Capitation, or other direct, Tax shall be laid, unless in Proportion to the Census or Enumeration herein before directed to be taken.” Art. I, §9, cl. 4. A tax on going without health insurance is not like a capitation or other direct tax under this Court’s precedents. It therefore need not be apportioned so that each State pays in proportion to its population. Pp. 40–41.
"It need not be apportioned" follows directly from the 16th amendment as this tax is a tax on income and not a direct tax covered by Art. I, §9, cl. 4. and income taxes are specifically exempted of the requirement that they be apportioned.