Nacional headed to Vasco's home ground in Rio de Janeiro two goals down from the first leg of their round-of-16 clash but struck from the penalty spot in just the seventh minute on Thursday to keep their hopes of progressing alive.
But Vasco recovered from the early blow and were level at half-time thanks to Marlone's strike, while Dakson gave the hosts victory in the 89th minute to wrap up a 4-1 aggregate win.
In Rio, Nacional stunned the home crowd when Erick Soares Rosa beat Vasco's Fillipe Soutto in the penalty area and then was brought down from behind by the midfielder.
Nacional's captain Danilo Rios had his spot kick saved by Vasco goalkeeper Diogo Silva but scored from the rebound to put the visitors ahead.
Jorge Henrique scored the visitors' opener in the first half before Ranieri pulled Salgueiro level in the 57th minute.
But in the 91st minute, Daniel Rodrigues Nazare slammed his left-foot shot past Internacional's goalkeeper Alisson to give the home side some joy despite their elimination.
