Speaking with DAZN, Bayern manager Julian Nagelsmann said his side "needed the crowd" to help them past PSG's "brutal quality" in the opening half.
"In the second half we were much better than our opponents and deserved to win."
Bayern captain Mueller said his team "had luck on our side" and credited "our mentality and our desire in the duels".
A disappointed PSG manager Christophe Galtier lamented his side's failure to "make the most of our chances" and conceding "a really stupid goal" through Verratti's error.
"There is frustration and disappointment in the dressing room. We can't repeat the match, we have to look ahead."
The best chance of a tight opening half fell to PSG's Vitinha, who won the ball when Bayern goalkeeper Yann Sommer attempted to dribble out of a busy penalty area.
Vitinha was presented with an empty goal, but his rolled effort allowed Matthijs de Ligt to clear the ball off the line.
Nagelsmann lauded De Ligt's intervention, saying: "it's incredible how much desire he has to defend. Nine out of 10 defenders in the world would have given up."
Bayern roared out of the blocks after half-time, but PSG were let off by the clumsy feet of Choupo-Moting, who tripped before shooting and then stood in the way of a goal-bound effort from Joshua Kimmich.
The Cameroon striker looked to have redeemed himself in the 52nd minute, but his header from a curling Jamal Musiala cross was chalked off for offside against Mueller.
Bayern continued to push and PSG's dam broke on 61 minutes, with Choupo-Moting doing the damage.
Mueller robbed the ungainly Verratti in the box, clipped the ball to Leon Goretzka, who squared for Choupo-Moting to double his side's two-legged advantage.
PSG centre-back Sergio Ramos had a chance to equalise just two minutes later, but his powerful header was brilliantly palmed away by Sommer.
With Kylian Mbappe and Lionel Messi experiencing off nights and Neymar sidelined by injury, Gnabry put the result beyond doubt, racing onto Joao Cancelo's pass before firing into the far corner left-footed.
Sadio Mane looked to have scored a third for the home side in injury time, but his effort was ruled out for offside.