The images of the shirtless young boys standing on the athletics track at the Vasil Levski national stadium caused a public outcry after being posted online. The children appeared to be well under 10-years-old.
Levski were defeated on penalties in the final by Slavia Sofia after neither side could score in 120 minutes of play.
The fine is equal to 37 average monthly salaries in the poorest country in the European Union.
Bulgarian soccer authorities have long been criticised by anti-racism campaigners, local media and fans for not cracking down hard enough on discrimination.
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Levski, one of the two most popular clubs in the Balkan country alongside bitter city rivals CSKA, have a history of fan violence and racism at their matches.
In 2012, The Blues were fined 30,000 euros (£26,218) by European soccer's governing body UEFA for racist behaviour by fans during a Europa League match.
The BFU fined the club 37,500 levs after supporters displayed a banner showing a swastika and another marking Adolf Hitler's birthday during a league game in 2013.
The 26-times Bulgarian champions were fined again in 2014 after fans displayed banners reading "Death to refugees" and "Blood will be shed for our land".
Some 40 Levski fans were detained after a policewoman was injured by a small explosion during a match last month.
(Reporting by Angel Krasimirov; Editing by Christian Radnedge)
