The BFU fined the 26-times Bulgarian champions £16,500 for racist abuse after their fans displayed one banner showing a swastika and another one marking what would have been Adolf Hitler's birthday.
The Sofia-based club were fined another £2,100 after supporters threw flares, fireworks and other objects.
"Levski and the national fan club distances itself from the actions of a small group of fans that raised banners during the match against Litex Lovech," the club said in a statement.
"We categorically declare that we'll not allow the football club and everyone who loves Levski to suffer in the future because of a handful of people."
Levski matches have a history of racism.
The Blues were fined £25,500 by UEFA for racism during a Europa League match in September but surprisingly escaped any sanction by the BFU when their Guinea-Bissau striker Bazile De Carvalho was racially abused by fans and stewards in August.
Levski are second in the standings with 52 points from 23 matches, two points behind champions Ludogorets.
Lowly Minyor Pernik have been ordered to play their next two home matches at a neutral ground following crowd trouble during their league game against Ludogorets on Sunday.
It is the second stadium ban for the Pernik-based side, who are 14th in the table, this season. Minyor were given a three-match ban following fan violence during their game against Lokomotiv Sofia in August.
The BFU also fined Minyor £4700 for the ugly incidents, in which a policeman was kicked by a fan while another supporter encroached on to the athletics track surrounding the pitch to protest against the referee's decisions.