Pumpido, who played for the team captained by Diego Maradona that won the 1986 World Cup, resigned on Sunday from Godoy Cruz after Saturday's 3-0 defeat by San Lorenzo left them with one win in 10 matches halfway through the Clausura championship.
"Unfortunately, cycles come to an end and mine's finished," the 54-year-old, who steered Paraguay's Olimpia to victory in the Libertadores Cup 10 years ago, told reporters on Monday.
Former Argentina coach Alfio Basile quit Racing Club at the weekend after the 4-1 derby defeat at Independiente.
The Clausura championship, second of two in the 2011/12 season, kicked off on February 10.
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