"I don't feel like continuing," Vercauteren said after the Group 5 match.
"I wanted to have 24 hours to think about it, but that would have achieved nothing. I prefer to stop straightaway," added the former Belgian playmaker, who was part of the side that reached the 1986 FIFA World Cup semi-finals.
Since the axing of previous coach Rene Vandereycken in April, Vercauteren had been keeping the seat warm until Dutch coach Dick Advocaat took over the reins on 1 January 2010.
Belgium, who had lost 5-0 to European champions Spain on Saturday, are fourth in the group with seven points from seven matches, 14 points behind the Spanish.