The 52-year-old Penev, one of Bulgaria's soccer icons, began his third spell at his former club in February after signing a one-and-a-half-year contract. He replaced Serbia-born Briton Nestor El Maestro.
"Three months ago I agreed to take over CSKA in a very difficult time for the club," the former Bulgaria coach said on Facebook.
"I had the great desire and will to do my best to achieve what CSKA deserve - a (league) title and the Bulgarian Cup.
"(But) the club's management did not stand behind me," he said, adding that he had faced "quiet but fierce opposition inside the club".
He ended his statement by saying he felt "very aggrieved" but left holding his head high.
Penev's announcement came a day before CSKA's away game against Cherno More Varna.
"I am surprised by the position of Lubo Penev, he had the support of the club management," CSKA’s chief executive Plamen Markov said.
"He puts us in a complicated situation, today the team is travelling, we play in Varna tomorrow."
Adored by CSKA fans, ex-striker Penev won two league titles and four Bulgarian Cups with CSKA as a player, scoring 88 goals in 123 matches.
With five matches remaining of the season, CSKA are second in the league standings with 65 points, five points behind champions Ludogorets.
Former defender Dobromir Mitov has been placed in temporary charge.
(Reporting by Angel Krasimirov; Editing by Toby Davis)
