The holders were left shocked as they failed to defend their 2-1 aggregate lead in the round-of-16 tie.
Having won in Amsterdam, Santiago Solari's struggling La Liga giants were favourites to go through, despite their troubled campaign.
But Los Blancos disastrous season peaked tonight as the Eredivisie giants turned on the style to prevail 4-1 winners in Madrid.
Welsh superstar Gareth Bale whose future is up in the air at the moment given his relationship with the Real fans, started the game on the bench.
The decision to axe him from the starting line-up came after his agent Jonathan Barnett branded Real supporters a "disgrace" for their treatment of Bale.
And it has emerged the man responsible for seeing them beat Liverpool in last year’s final but failing to make an impact tonight is on staggering sums of money compared to the Ajax players.
Bale is believed to be on wages worth up to €21m (R337m) a year at the Bernabeu in a contract that runs until the end of the 2020/21 season.
"At this level it is a different story," Overmars told AS before the game. "My player budget is 28 million euros (R449m), for the first, second and youth.
"That is just as much as Gareth Bale earns on his own. Real works with 630 million (R10bn). We can never match that. What Real pays for one player, we pay for the entire selection."