The former Brazil, Portugal and Chelsea coach made an insulting gesture and argued with the supporters who jeered the players and threw coins as they entered the tunnel following the game.
'Big Phil' then insinuated the supporters had been working with people inside the club to unseat him.
"The protest was ridiculous," he said. "Go and find out who let them into the training ground last week, who they were talking to and want they wanted. All this is well-orchestrated."
Avai took an early lead with a deflected shot by Batista and it got worse for Palmeiras when Rivaldo Barbosa was sent off for a second bookable offence in the 23rd minute.
Chico equalised before half-time but Palmeiras, who dropped to eighth in the table, were reduced to nine players early in the second half when Gerley was given a straight red card.
Shortly afterwards, Avai substitute Rafael Coelho was dismissed after only four minutes on the pitch.
Corinthians were knocked off the top, dropping to third, when they lost 3-1 to 10-man Santos, despite taking an early lead through former Portugal striker Liedson.
Henrique, later sent off, equalised before half-time and Borges, the championship's top scorer, gave Santos the lead with his 17th goal of the competition nine minutes into the second half.
Alan Kardec added a third late in the game for the South American champions.
Vasco da Gama's 4-0 win over Gremio took them top with 45 points from 24 games and Sao Paulo, one point behind, beat Ceara by the same score. Corinthians have 43 points.
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