The Parisians retained their crown with a 4-3 shootout success after a tense contest finished 1-1 following extra time in Budapest, becoming the first side since Real Madrid between 2016 and 2018 to successfully defend the trophy.
Yet despite securing back-to-back European titles, Luis Enrique insisted the final was so evenly balanced that neither side truly deserved to win on the night.
"It was a very tough match, a lot of suffering. Neither team deserved to win this match," said the Spaniard. "But if I analyse the season, we deserve to win our second Champions League."
The triumph adds to the title he won with Barcelona in 2015 and places him alongside Carlo Ancelotti, Bob Paisley, Zinedine Zidane and Pep Guardiola as the only managers to lift Europe's biggest club prize three times.
Luis Enrique also ranked this latest success above PSG's maiden Champions League triumph a year ago.
"It is even bigger because we knew of the difficulties of playing against Arsenal, and for us as a team and a city it is incredible to win it."
Arsenal struck first through Kai Havertz after six minutes, but PSG levelled when Ousmane Dembele converted a 65th-minute penalty after Khvicha Kvaratskhelia was fouled.
Kvaratskhelia later hit the post as Arsenal held on to force extra time and penalties.
Luis Enrique admitted his side initially struggled to break down Arsenal's defence.
"We struggled to find space. We improved in the second half. It's difficult to overcome. We managed to get a draw."
The PSG boss said his players remained calm during the shootout.
"The penalty shootout? We did it the usual way to decide the penalty takers. They chose among themselves who was the freshest to take the penalty. I watched the shootout calmly."
Nuno Mendes was PSG's only miss from the spot, while Eberechi Eze failed for Arsenal before Gabriel blasted over with the Gunners' final attempt.
Luis Enrique said the achievement was the reward for a season-long effort.
"We're in a dream. Very happy. This back-to-back win was incredible. It's time to celebrate. It's time for a holiday."
Gabriel Magalhaes said it was "painful" after missing the decisive penalty as Arsenal lost the Champions League final to Paris Saint-Germain in a shootout in Budapest.
Arsenal manager Mikel Arteta described Paris Saint-Germain as the best team in the world after watching his side suffer Champions League final heartbreak, but insisted the Gunners must respond with ambition in the transfer market.
Paris Saint-Germain etched their name deeper into European football history on Saturday, defeating Arsenal 4-3 in a dramatic penalty shootout to retain the UEFA Champions League crown in Budapest.
Raheem Sterling has been arrested following a motorway incident after his Lamborghini collided with barriers on the M3, adding to a difficult period for the former England forward.
