An early goal from Caroline Weir gave Real a head start, while late goals from Signe Bruun, Caroline Moller and Linda Caicedo sealed a decisive victory over Celtic.
Elena Sadiku's side may still look at it as a decent result as their hosts peppered the goal with 29 shots throughout a dominant evening.
Victory gets the Spanish side on the board in Group B after they lost in the opening round of fixtures, while Celtic have lost both of their games.
Scotland's Weir set the tone with a seventh-minute screamer for the hosts, rocketing a 20-yard effort into the back of the net.
TrendingIt was an onslaught and Celtic did well to survive to half-time without suffering further damage, with Las Blancas hitting the woodwork with a shot which deflected off Amy Gallacher.
They somehow held out until the 72nd minute when Bruun made it 2-0, heading home Eva Navarro's cross to finish off a fine team move.
Moller made it three 10 minutes from time when she saw Celtic goalkeeper Kelsey Daugherty off her line and chipped her.
The rout was completed three minutes later when Caicedo converted from the spot after she won the penalty being fouled by Shannon McGregor.
Here are Celtic's remaining fixtures: