The Belgium international, who spent seven seasons at Stamford Bridge before joining Madrid in 2019, was heavily criticised for sharing a joke with some of his former colleagues.
April 2012: Madrid Knocked Out of CL in Semi-Final— RMadridbabe (@RMadridBabe) May 5, 2021
April 2013: Madrid Knocked Out of CL in Semi-Final
May 2021: Madrid Knocked Out of CL in Semi-Final
Eden Hazard doesn't deserve to wear Real Madrid Jersey. #HazardOut pic.twitter.com/9xbDhdToau
It came after another ineffective performance from Hazard, who has struggled for injuries in his two seasons at the Santiago Bernabeu and has been linked with a move away.
He played 89 minutes of the 2-0 loss in west London as goals from Timo Werner and Mason Mount send perennial European champions Madrid crashing out 3-1 on aggregate.
🚨| Eden Hazard issues an apology to Real Madrid fans. 👏 pic.twitter.com/yD3BZIdZB3— Madrid Xtra. (@MadridXtra) May 6, 2021
A number of former Madrid players have taken aim at Hazard for his actions at full-time, with Fernando Morientes calling for the 30-year-old to say sorry to the club's fanbase.
And Hazard took to social media on Thursday to do exactly that in a short statement that read: "I am sorry. I have read lots of opinions about me today and it was not my intention to offend the 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 not battle for La Liga! Hala Madrid!"
Hazard won two Premier League titles, two Europa Leagues, the EFL Cup and the FA Cup during his time with Chelsea.
The forward has featured only 40 times for the Spanish giants in all competitions since arriving in a big-money deal, including 18 appearances in the 2020-21 campaign.
He may get an opportunity to redeem himself when title-chasing Madrid host Sevilla in LaLiga on their return to action on Sunday.