The reigning European champions raced into a 5-2 lead before Bayern clawed back to 5-4, setting up a knife-edge second leg in Munich.
"I think it was the best match I have ever managed as a coach," Enrique said. "It had amazing rhythm, trying to play offensive football, trying to show their quality. I think everybody had fun watching the match."
Enrique admitted he struggled to stay composed on the touchline as goals flew in from both sides.
"I think I achieved that for the first two or three goals, but after the fourth and fifth it was a mistake because I knew they could score again."
The Spanish coach was full of praise for the quality on display across both squads, namechecking Harry Kane, Michael Olise, Joshua Kimmich and Aleksandar Pavlović for Bayern, alongside PSG's Khvicha Kvaratskhelia, João Neves, Vitinha and Ousmane Dembélé.
"You can watch today those players, and if you look at our team — it was amazing. It is important to show that that is the way to try to play football."
Enrique acknowledged that conceding four goals is never acceptable, but found perspective in the result and the performance.
"Okay, we are not happy as a coach when you concede four goals, but today I'm happy because we won."
PSG's familiarity with Vincent Kompany's Bayern from three previous meetings this season informed their approach, though Enrique warned the return leg will demand everything from his side.
"We knew that with the rhythm, they would be very difficult to manage. Bayern Munich only lost one season three match, and the next match against them is going to be too tough, like this one."
The first leg record — nine goals, the most ever scored in a Champions League semi-final — will travel to Munich with the tie delicately poised.