Hiddink's men conceded in second-half injury time in calamitous fashion in Prague, Vaclav Pilar tapping in to an empty net after Daryl Janmaat's attempt to find goalkeeper Jasper Cillessen was wayward.
The World Cup semi-finalists had equalised earlier in the second half via Stefan de Vrij, cancelling out Borek Dockal's 21st-minute opener.
Hiddink was furious his side failed to take anything away from the fixture.
"I was livid," Hiddink said.
"I had to introduce myself to shelter. That's why I stayed away for half an hour.
"If you cannot win, you must be sure that you will not lose in any case. Then you should not be so stupid to give away [a goal]."
Hiddink lambasted Janmaat for his defensive error, and said Dutch errors led to the Czechs' opening goal also.
"When you make mistakes like that, then it is a very difficult story," he said.
"Whether you play football with four or five defenders, it does not matter if you're so naive defending.
"The first goal they shoot great inside, but for that we had to suffer two clumsy turnovers.
"That second goal we completely gave away."
Czech coach Pavel Vrba was thrilled to finally oversee his first win in charge of the national team since taking the reins in January.
Vrba admitted they were fortunate, after opting to play on the counter-attack after De Vrij's equaliser.
"I am thrilled, perfectly happy with the 2-1 win, although it wasn't easy and we were a bit lucky at the end," said Vrba, after his fifth match in charge.
"We scored a beautiful goal that helped us a lot. In the second half we waited, it would have been suicide to play in their half.
"We tried to succeed on the break and reaped the bonus of the winning goal."
