The Turin giants led 2-0 after 65 minutes only to concede four goals and lose 4-2 in Florence.
"The game was over," Conte said to Gazzetta dello Sport. "We were in control, we were dominating possession, we were 2-0 up and we had two further chances to kill the game off.
"Then the unthinkable happened.
"In 15 minutes we threw away all the good work we had done earlier."
Juve were left stunned by a 15-minute Giuseppe Rossi hat-trick that turned the game around.
"We had a nightmare that lasted 15 minutes and I hope this will be a lesson for my players,"
Conte said. "Football is like this and you cannot rule out anything.
"You always have to give 110 per cent."
The loss was Juve's first in Serie A and dropped the Italian champions to third place, five points
adrift of league leaders Roma.
Juve travel to the Bernabeu stadium on Wednesday to face Real Madrid in the Champions League looking for their first win having drawn their first two Group B games.