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.
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.
The top two teams, Fluminense and Ronaldinho's Atletico Mineiro, both fell to unexpected defeats.
Mineiro remain two points behind 'Flu' with a game in hnad after going down 1-0 at 12th-placed Nautico.
