The Brazilian team returned to Sao Paulo from Wednesday night's 2-0 defeat by Deportes Tolima in Colombia in the second leg of their tie having drawn 0-0 at home last week.
It was the first time a Brazilian team had failed to qualify from the preliminary round, while Tolima went through to the group phase.
Former Brazil striker Ronaldo was called a "shameless fatty" in one of the slogans painted on the walls of the club's headquarters. Others said "Ronaldo out" and "Ronaldo propaganda-kid" in reference to adverts exploiting the 34-year-old's image.
At the club's training complex, TV pictures showed players' imported cars being damaged by stones thrown by fans.
The only one of Sao Paulo's big clubs never to have won the Libertadores Cup, South America's elite club competition, Corinthians had already disappointed their fans in their centenary year in 2010. They were eliminated by fellow Brazilian side Flamengo in the quarter-finals having signed Ronaldo and Roberto Carlos for a tilt at the title.
"This is a defeat we're going to have to carry for the rest of the year," former FIFA World Player of the Year Ronaldo, in the last season of his career, told reporters at the end of Wednesday's match.
