PSG won 4-3 on penalties after a 1-1 draw in Budapest, becoming the first club to retain the European title since Real Madrid's three consecutive victories between 2016 and 2018.
Kai Havertz had given Arsenal the lead in the sixth minute before Ousmane Dembélé's second-half penalty levelled. The shootout was won when Gabriel Magalhães sent his final effort over the bar.
Speaking to TNT Sports, Enrique framed the win in terms of the full campaign rather than the single match.
"I think we deserve — maybe today both teams deserved to win — but the way we played the whole season, I think we deserve to win the Champions League. We are very happy and trying to be there next year — why not?"
On the specifics of the final, he acknowledged the difficulty Arsenal posed.
"The match started in the best way for them. After that, they know how to defend. It was very tough. We are used to attacking in that way with a lot of players behind the ball, but against them, they are strong physically, very tough."
He described his feelings at full time with typical directness.
"I'm mixed. Excitement, fatigue. Everything. But this is the best moment of the season. We are still champions, two in a row, it's amazing. We deserved that. Our supporters, during the whole season. Congratulations to Arsenal, it was very tough. They played great. It's normal. They try to take the match into phases they are strong. We tried to control the ball and press. We have won the title."
Asked whether being regarded as a legendary manager now sits with him, Enrique was characteristically brief: "Legend? I'm not interested in that."
PSG beat Liverpool, Aston Villa and Bayern Munich before defeating Arsenal in the final to complete the defence of their title. Dembélé's penalty was his 33rd goal contribution of the season, reinforcing his position as the frontrunner for a second consecutive Ballon d'Or.