Coach Bert van Marwijk, who named his 23-man squad for the tournament earlier in the day, suffered his first setback after 15 minutes when central defender Joris Mathijsen limped off and was replaced by Wilfred Bouma.
"Joris felt something in his hamstring and wanted to avoid any risk" Van Marwijk told reporters.
"But according to the medical staff it looks like he pulled his hamstring and no tearing.
"It was an annoying match especially after the penalty, before that we did everything well although we did not create a lot of chances.
"That had to with the choices we make and the pace in passing, but in the final half-hour we did everything wrong and dropped our organisation completely."
The Dutch never got striker Klaas-Jan Huntelaar into the game but after Valeri Bojinov had hit the crossbar with a 20-metre free-kick for Bulgaria, Robin van Persie opened the scoring for the Dutch.
Ivelin Popov equalised early in the second half from the penalty spot after a handball by Rafael van der Vaart.
The Dutch brought on Bayern Munich forward Arjen Robben in the final 15 minutes but defensive sloppiness allowed the unmarked Mizanski to head the winner at the near post in stoppage time.
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