Chelsea advanced to the final 3-1 on aggregate and will meet Manchester City in Istanbul later this month.
Hazard, who spent seven seasons with Chelsea, winning two Premier League titles, two Europa Leagues, one FA Cup and one League Cup, was seen in a hearty chat with his former colleagues after the final whistle, which has not gone down well with a lot of the Real Madrid faithful.
"It’s really not smart for Eden to do that,” Courtois’ father, Thierry, told the HLN Sportcast podcast.
"He probably didn't think twice about it, but those images are painful for Real Madrid fans.
"If you see a player laughing two minutes after being eliminated, I'd say it was unprofessional."
Meanwhile, Hazard has apologised to the Real Madrid fans for his actions in a post on Instagram, which read: "I am sorry. I have read a lot of opinions about me today and it wasn't my intention to offend Real Madrid fans.
"It has always been my dream to play for Real Madrid and I came here to win.
"The season is not over and together we must now battle for La Liga. Hala Madrid!"