Atletico Madrid's stunning 1-0 success at the Calderon sealed a 2-1 aggregate success for Diego Simeone's outperforming side and sent them through to the last four of Europe's elite club competition for the first time in 40 years.
They lead second-placed Barca by a point in La Liga with six games left and are within touching distance of a first domestic league triumph since a team featuring Simeone won a La Liga and King's Cup double in 1996.
Simeone's tired troops have a mere three days to recover before facing a Getafe side in 18th and battling to preserve their top-flight status.
Champions Barca, who are chasing a fifth title in six years and host Atletico Madrid on the final day of the season, face a similar task at 15th placed Granada on Saturday, when Real Madrid, three points behind Atletico Madrid in third, will be confident of victory at home to 19th-placed Almeria.
Simeone is waiting on the fitness of his top scorer Diego Costa, who missed the Barca game along with injured playmaker Arda Turan after failing to shake off a thigh strain.
Adrian, who has barely featured this season, replaced Costa in the starting 11 and turned in an excellent performance, providing the headed assist that set up Koke to volley Atletico Madrid's winning goal in the fifth minute.
"I was very pleased with his (Adrian's) game," Simeone told a news conference.
"We need him and today, above all in the first half, he played to his potential," added the Argentine.
"Hopefully in the final weeks of La Liga he can give us what the team requires."
Wounded Barca, meanwhile, need to pick themselves up after to failing to qualify for the Champions League semi-finals for what would have been a record-extending seventh consecutive season.
Their fate in La Liga is in their own hands and six wins would secure the title for Gerardo Martino's side in the Argentine coach's first season in charge.
They can also claim the King's Cup by beating arch rivals Real in Wednesday's final in Valencia.
Barca playmaker Andres Iniesta said he and his team mates cannot afford to let their reverse in Europe affect their progress in the two domestic competitions.
"The pain is real today and tomorrow but that's what happens in football and sport," added the Spain international.
"We will carry on and try to win everything that is still open to us."
Real, who qualified for the Champions League semi-finals when they scraped past Borussia Dortmund on Tuesday, are expecting to have La Liga top scorer Cristiano Ronaldo back for the Almeria game.
The Portugal captain, who tops the scoring chart with 28 goals, three more than Costa and Barca forward Lionel Messi, has a left knee problem and was rested for the Dortmund match.