The former Eintracht Frankfurt boss has dismissed criticism of his shot-stopper, who raced off his line towards Mane with the scores tied at 0-0 before the Senegalese forward rounded him and dinked the ball home.
"A goalkeeper has to come out at this moment, to stop the striker eventually passing through," Kovac said after the game.
"Manuel's decision was the right one."
Neuer, too, defended his actions, claiming that it was the Senegalese's brilliance, rather than his error, that led to the goal.
"Mane is in the inside channel and is running towards me, and I thought I could put him off," Neuer said after the full-time whistle.
"If he takes a normal touch, I get the ball, but he takes a world-class touch so the ball is right in front of his feet. He makes a body feint, goes around me and chips the ball into the goal.
"If I had stayed in goal, Mane would have been one-on-one against me and had a clear chance to score."
Bayern equalised after that goal, as former Arsenal winger Serge Gnabry's dangerous cross was turned into his own net by Joel Matip, but were then twice pegged back as Virgil van Dijk headed in a corner and Mane grabbed a second.
And despite his defence, Neuer may feel concerned that he could be next on the national team chopping block, after seeing Joachim Low call time on three of his team-mates' international careers - Thomas Muller, Mats Hummels and Jerome Boateng - and with many calling for Barcelona's impressive Marc-Andre ter Stegen to take his place between the sticks.
The Bavarians return to Bundesliga action this weekend, with Mainz set to arrive at the Allianz Arena as the German title race continues.