Roy Hodgson’s men were comprehensively dominated in the first half of the tie after conceding four goals in a space of 22 minutes.
Goals from Nacho Monreal, Alex Iwobi, Laurent Koscielny and Alexandre Lacazette rendered Luka Milivojevic’s second half’s effort a mere consolation.
The defeat is their 11th in the league this season which leaves them in 13th place.
“Not a good day of course but these things happen ... let’s focus on next chapter and take the few positives of today,” Sako tweeted.
Palace will be hoping to bounce back when they meet London rivals West Ham United on January 30.