Mbappe scored his side's first, second and fourth goals on the night and then opened up on his future with the Ligue 1 champions after the match.
"I have always said that I am happy here. This sort of match makes me even happier. The PSG shirt is one that I hold dear to my heart," the France international told RMC Sport in a postmatch interview.
"I am happy. I always want to give the best of myself. I have not always had that success but never in my life will I hide. Today, my hard work is paying off."
Mbappe also denied rumours that losing to Barcelona on Tuesday would have meant him not extending his contract with the club. His deal expires in June of 2022.
"It would be stupid to decide my future on a single match. The truth is that it is about reflecting for the long term," he said.
Tuesday's heroics made the 22-year-old the first player to score a Champions League hat trick at the Camp Nou since Andriy Shevchenko in 1997. It was the first time he had faced the Catalans, and played at their ground, in his career.
"Kylian shone tonight. Everyone is happy with his performance. When Kylian shines in the big matches, he makes the difference. He brought us this victory," PSG captain Marquinhos said after the game.
Barcelona forward Antoine Griezmann was also full of praise for his France teammate.