The 26-times Bulgarian champions want the BFU to award them a 3-0 victory in the first leg of the round-of-16 tie.
"Any other decision would be in flagrant contradiction with the general principles laid down by FIFA and UEFA," Levski said in a letter sent to the BFU on Wednesday.
"Moreover, it will set a precedent that will ensure impunity for clubs who refuse to release players for national teams."
CSKA midfielder Ivaylo Chochev was included in the Bulgaria Under-21 squad for the European qualifiers against Denmark on Friday and Slovenia on Tuesday but the club refused to release him because of the "eternal derby", as matches with Levski are known.
"We would like to inform you that CSKA will not release midfielder Ivaylo Chochev for the Bulgarian U-21 team's qualifiers because the dates of the matches coincide with our Bulgarian Cup game against Levski Sofia," the club said in a statement earlier this month.
Chochev, 20, is considered one of the best young players in the Balkan country.
The second leg of the Bulgarian Cup tie will take place on Dec. 19.