Palmeiras announced last week that Scolari, who coached Brazil to the 2002 World Cup, had parted ways with the club after a series of defeats left them mired in the Brazilian championship's relegation zone.
"He asked to leave (and) it was a surprise to us," Chilean Valdivia told reporters after Palmeiras suffered a 2-0 defeat by Corinthians on Sunday under caretaker coach Narciso.
"He had told the squad that if we went down he would go down with us, but after the match with Vasco he informed (the club) he was quitting," added Valdivia.
Sunday's loss in the Sao Paulo derby, in which Palmeiras had striker Luan sent off in the 26th minute for a second booking, left Palmeiras in 19th place in the 20-team league with 20 points from 25 matches.
The bottom four teams face relegation at the end of the season, which has 13 rounds to run.
Scolari, a former national coach of Portugal and of English Premier League heavyweights Chelsea, took Palmeiras to victory in the Copa Brasil, the country's knockout competition, only two months ago.
He previously coached Palmeiras in a highly successful stint from 1997-2000 in which they won the Brazilian championship, Copa Brasil and the South American club championship, the Libertadores Cup.
He has been seen as a possible replacement for Brazil coach Mano Menezes who, despite winning most of his games in his two years in charge, has failed to capture the public imagination in the run-up to the 2014 World Cup, which Brazil hosts.
Romarinho and Paulinho scored the goals for champions Corinthians, who are ninth in the standings after a slow start from having prioritised the Libertadores Cup. Corinthians won that tournament to qualify for the Club World Cup in December.
The top two teams, Fluminense and Ronaldinho's Atletico Mineiro, both fell to unexpected defeats.
Fluminense retained their lead in the championship with 53 points despite a 2-1 upset at home by bottom team Atletico Goianiense, who notched only their fourth win in 25 matches.
Mineiro remain two points behind 'Flu' with a game in hnad after going down 1-0 at 12th-placed Nautico. (Writing by Rex Gowar; Editing by Ian Ransom)