Moussa Diaby’s goal gave the Bundesliga side a 4-1 aggregate victory and they will take on Inter Milan in the quarter-finals.
All eyes were fixed firmly on Havertz as he has told club bosses he wants to leave to join Chelsea.
The Blues have apparently agreed personal terms and are working on the fee with Leverkusen demanding £90million.
The German side want to keep their versatile midfielder until their Europa League campaign comes to an end.
And Bosz has explained how he has attempted to protect Havertz – although he has backed the star to handle the pressure.
“We are watching all this closely,” Bosz told DAZN and Goal. “Of 20 interview requests, 18 want to speak with Kai. Then we must make sure he doesn’t go 18 times.
“He is an exceptional player, but even exceptional players can have a bad day. If we lose, he is always the first to be criticised, even if he didn’t play that badly.
“I often talk to him and explain how I saw his game. Then there are games like the one against Hertha Berlin, when the fans whistled at his substitution.
“I told him that maybe he learned the most in that game, where he was really not good.
“But Kai is an intelligent boy overall and knows how the world works.
Meanwhile, Manchester City’s Ilkay Gundogan has tipped his international team-mate Havertz to have a glittering career.
“In my opinion, Havertz is even better than [Michael] Ballack in terms of his playing ability,” Gundogan told Sport Bild.
“Ballack had a certain level of aggression in his game, and a strong mentality.
“He was a top player of the previous generation – a b*****d on the pitch, in a positive sense. Kai isn’t like that.”
If Havertz arrives at Stamford Bridge over the coming weeks he will be the third addition of the summer following the transfers of Hakim Ziyech and Timo Werner.