Levski played most of the last-16 game with 10 men after Moroccan defender Youssef Rabeh was sent off for a robust tackle in the 14th minute.
Levski substitute Hristo Yovov was also shown a red card by referee Stanislav Stavrov in the first half for invading the pitch to protest against a disallowed goal.
Levski coach Georgi Ivanov was dismissed during halftime and police had to keep him away from Stavrov, the latest in a string of disciplinary problems which have marred Ivanov's coaching career.
"It's ridiculous," said Ivanov, who was sent off for the second time in less than three weeks. "It's a pity. I'm afraid that the championship will not finish in the spring if they (referees) continue officiating like this."
Levski's fan club said in a statement later that fans would be gathering in downtown Sofia on Monday to protest against the Bulgarian Football Union (BFU) and the referees.
BFU president Borislav Mihaylov said its executive committee would be holding an extraordinary meeting to discuss recent incidents in domestic matches.
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