The Spanish capital rivals go into the semi-final tie's second leg at Vicente Calderon with Real 3-0 up on aggregate, leaving Atleti facing a mountain to climb if they are to retain the crown they won last term.
However, Atleti will have plenty to play for, if they use the clash as a dress rehearsal for the sides' league derby on March 1.
That game takes on huge significance given the incredibly tight nature of the title race in La Liga.
Diego Simeone's side led the league outright for the first time since 1996 after beating Real Sociedad last weekend, but were knocked off that perch on Saturday as they slumped to a 2-0 defeat at Almeria, while Real moved above them courtesy of a 4-2 win over Villarreal.
Atleti midfielder and captain Gabi - who ended the Almeria defeat in goal after Dani Aranzubia was sent off - has challenged his colleagues to snap their bad run immediately.
"The team is gutted," he said. "But you have to raise your head, work harder if possible to remove this slump soon after two matches. Let's see the power this team has overcome it.
"Now we have to be united more than ever.
"We have been in a privileged position and we are lucky to still be there and we will fight because this little bad run is costing us points."
Atleti won at the Bernabeu earlier this season, their first league triumph over their neighbours in the 21st century, as well as last season's Copa final - but the sides' head-to-head record is massively stacked in Real's favour.
Real will take further confidence with Cristiano Ronaldo likely to return to their XI as his Liga suspension does not affect his Copa availability.
The Portuguese star could be reunited in attack with Gareth Bale - who returned from a calf injury with a goal and assist against Villarreal.
Atleti will be without Tiago, who suffered a sprained knee against Almeria, with David Villa (hamstring) and Filipe Luis (groin) also sidelined.
One bright spot for Simeone will be the return of Koke, available again after suspension forced him out of the weekend's defeat.
