Having fallen behind to a first-half strike from Didier Drogba, the Bianconeri levelled a dramatic Champions League clash on 78 minutes when Arturo Vidal fired home from 12 yards out, after Quagliarella had tumbled in the area under a challenge from Nordin Amrabat.
Galatasaray boss Roberto Mancini labelled the decision to award a spot kick "strange" - but the man at the centre of the controversy dismissed the implication that he had dived.
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"There was contact, and I could not stay on my feet - it was a clear penalty."
Quagliarella subsequently put Juve ahead with a powerful header only to see Galatasaray level just 60 seconds later to deny their hosts a first win in Group B.
"It was a shame," the former Napoli striker lamented. "We were ahead four minutes from the end.
"They had two shots and scored two goals. The game had always been in our hands.
"We should have won. When you go ahead with four minutes left and concede an equaliser straight away, it leaves a very bitter taste in your mouth."
After another impressive Champions League cameo, Quagliarella is now hoping to nail down a regular berth in Antonio Conte's starting line-up, though the 30-year-old insists that he is still prepared to bide his time.
"The coach knows that he can count on me," he reasoned. "Sometimes it goes well, others bad, but the important thing is to always be ready."
Despite having drawn their opening two fixtures, Juventus still sit second in their group, but they are already four points adrift of leaders Real Madrid, whom they face next.