A four-time national champion, Fluminense is desperate to avoid becoming the first defending champion to be demoted in the Brazilian league. The club also won the title in 2010.
The loss on Sunday came after Fluminense conceded a last-minute penalty that Corinthians striker Alexandre Pato converted. A week ago, Fluminense also conceded a last-minute own goal in the loss to rival Flamengo at the Maracana Stadium.
Some fans protested after the loss to Flamengo by invading the team's headquarters. They vandalized one of the training fields, destroyed sponsors' billboards and damaged cars in the parking lot, including some belonging to players.
Luxemburgo leaves the team with 36 points from 33 matches, one point less than rival Vasco da Gama, the first team out of relegation zone. Criciuma has the same 36 points as Fluminense but is ahead on number of victories. Ponte Preta is behind with 34 points, while already relegated Nautico has 17.
Fluminense hosts Nautico this week and Sao Paulo over the weekend.
Luxemburgo had been saying he would not quit despite the team's struggles and hoped that three victories in the final matches could be enough to avoid the team's first relegation since the late 1990s.
Luxemburgo took over Fluminense in July after Abel Braga was fired following a streak of five straight losses in the league. The team was 17th in the standings at the time. Fluminense won seven matches, drew nine and lost 10 under Luxemburgo.
The coach said political reasons might have played a role in his departure.
"I respect the decision because I know there is political process under way and elections are coming up at the club," he was quoted as saying by GloboEsporte.com
One of the reasons for the team's recent struggles is the absence of Brazil striker Fred, who has been nursing a right muscle injury since September. The team is hopeful he will return by the end of the year, but it remains unclear exactly when.
Fred was part of the Fluminense team that escaped relegation with a remarkable run in 2009, winning six of the last seven matches to barely remain in the top flight.
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