The former Tottenham forward hit a hat-trick, with an injury-time winner sending Ireland into the World Cup qualifying playoffs.
He told BBC Sport a day later: "How many times I have watched it back? Probably about 500 times - every time I go on to my phone, it's there.
"Even last night when I got to bed, I couldn't sleep imagining it over and over and over again.
"In general, I'm not really an emotional person, it's the first time I've cried in years. Look I can sit here and try to describe it, but it is the first time I've felt something like that.
"I've scored goals before but none as meaningful as my last one against Hungary. As a country we've had a lot of disappointing results and haven't given the fans a lot to cheer about, so this was tears of joy."
Tough career start
Parrott admits the night was a pinnacle in his burgeoning career.
"Part of the celebrations last night was that up to this point in my career it hasn't been so easy," Parrott explained.
"I've had to take risks in moving to different places. I've failed, got back up. Failed again and then got back up. Who is to say I'm not going to fail again?
"I feel the tough road I have had definitely played a part in last night. Moving to the Netherlands gave me a sense of being wanted, I felt appreciated and sometimes for a player that's all they need.
"I know playing in England didn't go so well and believe me I really beat myself about it at the time.
"So when it came to thinking about moving away, I thought: 'What is the worst that can happen?'
"And I really love it, I feel appreciated, I feel out of the spotlight which I never had for a few years."