Robert Mak stunned the Olimpiyskyi stadium with a fine goal after 17 minutes, finishing with a shot into the corner of the net after being put through by Slovakia captain Marek Hamsik.
Pyatov thought he had equalised when he went up for a corner but was penalised for fouling his opposite number Matus Kozacik before hooking the ball over the line in the Group C clash.
"We scored a fair goal in the end and I was surprised the referee cancelled it," said Ukraine coach Mykhaylo Fomenko.
"We did not foul in the penalty area, Slovakia's keeper simply collided with his team mate.
"We had at least three key players missing due to injuries which affected our performance," he added.
Slovakia dominated the first half and after Mak had scored they came close to doubling the lead when Jan Durica headed over from close range and Peter Pekarik's curling shot was saved.
Ukraine came to life when Brazilian-born Edmar headed against the far post and later wasted another chance by diverting the ball over the bar.
Scottish referee Craig Thomson then infuriated the home side with his decision that one goalkeeper had fouled the other, condemning Ukraine to defeat.
(Writing by Igor Nitsak; Editing by Steve Tongue)
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