Avai, who led 2-1 after 40 minutes, had defender Para sent off for a second booking before halftime and Palmeiras equalised in the 55th minute.
However, a penalty by midfielder Caio, his second goal of the match, and a strike from Roberto in stoppage time handed Avai a surprise win on Sunday.
"The responsibility for the substitutions is mine, I was the one who lost," Scolari said.
"We tried and wanted to win and for that reason we made changes which ended up being more effective for our adversaries. Our midfield was open and gave Avai room," he told reporters.
"We still have to build a playing system so we can be calm, winning, losing or drawing the occasional game. We need patience."
Scolari, who steered Palmeiras to the South American Libertadores Cup in 1999, had made a winning return on Thursday with a 2-1 home win over Santos. The 61-year-old returned to the club after spells with Brazil, including a World Cup victory in 2002, Portugal, Chelsea and Bunyodkor of Uzbekistan.
Corinthians are two points clear at the top after beating Atletico Mineiro 1-0 while promoted Ceara, who had shared the lead, lost their unbeaten record in a 2-1 away loss to Internacional and dropped to third. Surprise team Ceara had conceded only one goal in their previous eight matches.
Fluminense climbed to second, two points behind Corinthians, with a 1-0 away win over Santos.
Unbeaten Corinthians have 21 points after nine matches, "Flu" 19 and Ceara 18. Avai are sixth with 14, Santos ninth with 12 and Palmeiras 11th also with 12.
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