 On 30 April 2014, Costa akakunda uye akashandura chirango muchikamu chechipiri cheChampions League semi-fainari neChelsea, sezvo Atlético yakakunda 31 kuStamford Bridge uye yakakwidziridzwa kumagumo emakwikwi kekutanga kubvira 1974. Akapedza mwaka weligi aine zvibodzwa makumi maviri nezvishanu zveligi kuti ave wechitatu wepamusoro zvibodzwa, uye timu yakahwina mukombe kekutanga kubvira 1996, asi akatsiviwa mushure memaminetsi gumi nematanhatu emutambo wekupedzisira wemwaka neBarcelona nekuda kwekukuvara kwehamstring. Atlético yakatsvaka kurapa kukuvara uku pamberi pekupedzisira kweChampions LeagueneReal Madrid nokumuendesa kuBelgrade kunorapwa neplasenta yebhiza, uye akabatanidzwa mumutsara wokutanga wemutambo unogumisa. Zvisinei, akasiya munda mushure memaminitsi masere mukurasikirwa kwekupedzisira 14; maneja Diego Simeone akazobvuma kukanganisa kwake pakusarudza mutambi kuti atange magumo kunyangwe akakuvara nguva pfupi yadarika. Costa akarova zvibodzwa zvisere panguva yeChampions League, achienzanisa rekodhi rakabatwa naVavá kubvira 1959 yevakawanda mumwaka nemutambi weAtlético, uye mune rake rese basa aive pakati pevatambi gumi veAtlético vepamusoro nechinangwa chepakati. Mumwaka weLFP Awards, akasarudzwa semutambi akanakisa weligi, achirasikirwa naCristiano Ronaldo. 