In his first Bundesliga match in the Bayern dugout, Kompany's side held a 1-0 half-time lead but were 2-1 down in the second-half, before turning the match in their favour.
Telling broadcaster DAZN he "enjoyed his first Bundesliga game as coach", Kompany said Bayern's mindset carried them to victory.
"We were dominant in the first half and didn't concede any chances. The start of the second half wasn't good.
"We conceded twice, but in the end the mentality was good and that's why we won the game.
"I played football long enough and know that you can lose or draw such a game. The fact we won shows that the mentality was there, even though not everything was perfect."
Speaking with reporters after the game, Kompany lauded Bayern's "outstanding mentality", saying "you can make mistakes but it's about how you react after the mistakes.
"We got the goals because we created the chances. A tough, tough away game but in the end a very good win."
England captain Harry Kane was again crucial for Bayern, with a hand in each of the visitors' three goals.
Kane played a key pass in the lead-up to Jamal Musiala's opener. His second-half header forced Wolfsburg into conceding an own goal and his pinpoint assist created Serge Gnabry's 82nd-minute winner.
"It's not perfect yet", Kane told Bayern TV after the match, saying his side "got punished a little" in the second-half.
"We're still obviously implementing some of the ideas of the coach.
"Obviously, the team is a lot stronger than this. I'm happy we've got a good week to work now, to get to work on the ideas the coach wants."
Next up, Bayern host Freiburg in Munich on Sunday.
