Juan Ignacio Martinez's side secured a 4-1 extra-time victory to clinch a 5-4 aggregate win in their fourth-round tie, but the night was soured by Juanlu's injury.
Coach Martinez was quoted as saying at his post-match press conference: "The injury to Juanlu tarnishes it all. These are things in football. The boy is sad. It is a shock for him."
The Malaga-born 31-year-old, who has scored six goals in the Primera Division this term to help his side to fourth spot heading into the winter break, is expected to be sidelined for around four months.
"Whenever there is a serious injury such as this, you get annoyed," Martinez added. "We will try to recover as soon as possible."
Nabil El Zhar, Sergio Ballesteros and Ruben Suarez all netted in normal time for Levante last night, with Depor's Pablo Alvarez also on target in the all-La Liga clash.
That left the scores level after 180 minutes, leaving Arouna Kone to seal it 11 minutes into the first period of extra time.