The LaLiga club alleged Barcelona used an ineligible player in the first leg of the last-16 tie, but their appeal was rejected by the Royal Spanish Football Federation (RFEF).
Levante beat Barca 2-1 at home in the first part of their two-legged clash, as Ernesto Valverde shuffled his pack, giving games to fringe players and youngsters.
Among the unfamiliar names in the starting XI was defender Chumi, who Levante believed to have been suspended for the match after accumulating five yellow cards for Barca's 'B' team in the third tier.
Barca were convinced Chumi was eligible, with Valverde suggesting the defender's suspension was active for Sunday's win over Eibar, while the club understood a rule change in November meant a reserve player can feature for the first team in another competition as long as the suspension is less than a two-match ban.
However, the RFEF ultimately rejected Levante's appeal due to their complaint being lodged too late.
But Levante announced on Monday they would take their appeal to the CAS.
"Levante will file an appeal with the Court of Arbitration for Sport," the club wrote on Twitter.
El #LevanteUD presentará recurso ante el Tribunal de Arbitraje Deportivo del Consejo Superior de Deportes tras la resolución del Comité de Apelación de la @rfef que confirma el archivo de la reclamación por alineación indebida del @FCBarcelona_es en los octavos de #CopadelRey.— Levante UD (@LevanteUD) January 21, 2019
The draw for the quarter-finals has already been made, with Barcelona set to play Sevilla in the first leg of their tie on Wednesday.