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McGinn, 28, came off the bench to hammer home his side's second goal in injury time, after Gareth McAuley had headed in the opener on 49 minutes.
"I don't think it has sunk in yet," McGinn told BBC Radio Ulster.
"What a night and what an occasion. To come off the bench and to score as well was just unbelievable for me."
Northern Ireland's victory, which keeps alive their hopes of reaching the last 16, was their first at a major tournament finals for 34 years.
A draw against world champions Germany in Paris on Tuesday will guarantee them a place in the knockout stages, though the three points they already have could be enough.
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McGinn said his goal was down - in part - to the pre-match warm-up at the Stade de Lyon.
"Before the game, I was hitting shots into those goals and hitting them nicely," said the Aberdeen winger.
"Josh (Magennis) got on the ball and beat the full-back and pulled it back. Stuarty (Stuart Dallas) shouted to me to leave it for him but I followed up the rebound.
"I was just in the right place at the right time."
Tyrone man McGinn said the team had gone into Thursday's game determined to regroup from Sunday's opening defeat by Poland.
"After the Poland game, we owed the fans, we owed ourselves a performance," he said. "We played on the front foot and we created a lot of chances.
"To a man, it was just an all-round perfect performance."
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McGinn said Michael O'Neill's side would take "great confidence" from their performance into Tuesday's match against the world champions.
"Even looking at the Ukraine v Germany game, we watched the highlights of that and Ukraine created a lot of chances," he said.
"On the night, if everything comes together and we get a wee bit of luck, hopefully we can nick a goal or two."
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Niall McGinn was still "on cloud nine" the morning after scoring a late goal in Northern Ireland's 2-0 Euro 2016 victory over Ukraine.