Bulgaria suffered the embarrassing defeat in a friendly on Wednesday and local media predicted it could lead to the 51-year-old's departure.
However, the former CSKA Sofia coach refused to consider stepping down.
"I don't know why they're always talking about resignation," he said. "I doubt that coaches' resignations will sort matters out.
"Bulgarian football doesn't have the potential that we want to have. But I'll continue my work and I hope that we will achieve some better results."
Markov previously quit as coach after the Euro 2004 finals in Portugal where Bulgaria suffered three defeats, but was reappointed in January.
Bulgaria managed only three lacklustre draws in their 2010 World Cup qualifying matches that preceded the embarrassing defeat in Belgrade.
Local media and fans have once again blamed Markov for the "ridiculous and unforgivable loss", but the Bulgarian football authorities decided the blame lay with the players, not Markov.
"He has our backing and I see no reason to discuss this issue," said Bulgarian Football Union's Vice President Yordan Lechkov.
Last month, Lechkov criticised some of the team's leading players, including Manchester United's Dimitar Berbatov, for their lack of enthusiasm.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
