Juan Carlos Osorio named Rafa Marquez, 39, as captain to make it five World Cups the veteran defender had skippered his country, but he was removed for Miguel Layun at half-time, with Brazil ending the first half on top. Neymar has scored two goals in this years' World Cup tournament, and will look to add to that number when Brazil plays the victor of Japan versus Belgium.
Mexico never really looked likely to get back into the game, and Brazil made sure two minutes from time.
O'Neill even said that Neymar's "play acting" is taking away from his otherwise impressive performances at a World Cup tournament in which he has now scored twice.
Mexico's poor run started from 1994, where they lost to Bulgaria 3-1 via penalties.
Shocks, mishaps and curiosities have arguably defined this World Cup so far but the tournament needs Neymar.
As Mexico threw bodies forward in search of a late leveller, Brazil took full advantage of the gaps in their backline to score a second with two minutes remaining.
While Layun didn't receive a caution for his action, he clearly stepped on Neymar and enabled a stoppage that halted some of Mexico's momentum. "I think this is a real shame for football, especially for kids who are watching because this has to be a sport of virility, of determination, a man's sport, like other games, and not a charade".
The awkward moment from Neymar came in the 71st minute when went down by the touchline when the ball was out of play and between his stretched legs.
As social media platforms exploded with fans angrily accusing Neymar of cheating, former England striker Alan Shearer described the Paris Saint-Germain star as "absolutely pathetic".
Belgium or Japan, who lock horns at 7pm this evening, await them in that last-eight clash in Kazan on Friday night.
Neymar powered through and his low effort was diverted into the path of Firmino, who had the simple task of tapping into an empty net. "We were maybe not very efficient and we didn't have that extra quality that they had coming to our goal".
Tom Marshall, a reporter for ESPN who covers the Mexican team, wrote on Twitter shortly after the match that Brazil, with its "elite players at elite clubs", was "simply too much" for El Tri.
Belgium and Japan face off later in the day, with the victor facing Brazil on Friday.