Kovac returned to Frankfurt for his first competitive game in charge of the Bundesliga winners, having ended two successful years at Eintracht with a shock win over Bayern in last season's German Cup final.
Yet there was no time for sentimentality on Sunday, as Bayern took brutal revenge for their cup humiliation, Lewandowski leaving the Frankfurt defence in tatters.
"It was a really good performance today, we scored at all the right moments," Kovac told ZDF.
"Of course I feel some sympathy for my former players and my former club, but I think it will still be a good season for Frankfurt.
"I am very optimistic for this season. I have a great team and a lot of strength in depth."
A ruthless Bayern took the lead with their first chance on 21 minutes.
Joshua Kimmich's cross picked out Lewandowski at the far post and the Polish star fired a header across Frederik Roennow in the Frankfurt goal.
The striker nodded in a second from almost exactly the same position five minutes later, heading Arjen Robben's corner past the stranded Roennow.
The game could have turned in Frankfurt's favour just before half-time when Mats Hummels escaped with a yellow card after bringing down Mijat Gacinovic in front of goal.
At the other end, Lewandowski faced increasingly rough treatment from the Frankfurt defence, and Eintracht captain David Abraham was also lucky to escape a red card when he appeared to elbow the Polish striker late in the game.
There was no stopping Lewandowski, however, who danced free of Abraham to rifle in his third goal on 54 minutes.
Kovac's perfect evening was sealed in the 63rd minute when Kingsley Coman bundled in Bayern's fourth.
The new Bayern coach had focused on low crosses in training the week before, and watched happily on as David Alaba's low cross found Coman at the far post to make it 4-0.
Thiago delivered the final flourish five minutes from time, gratefully receiving a pass from Coman to slot home Bayern's fifth.
Sandro Wagner could even have made it six, missing an open goal from two yards out, but that didn't stop Bayern celebrating a winning start under Kovac and a successfully defended Supercup title.