Litex were knocked out of the competition by unfancied Lithuanian side FK Jelgava on the away-goals rule after both legs produced a 3-3 aggregate score.
"It was not easy to take this decision but in the end the results are more important than anything else," former Bulgaria midfielder Balakov, who took charge of Litex on a two-year contract in May 2014, told local media on Friday.
Capped 92 times by the Balkan country between 1988 and 2003, Balakov had previously coached Swiss clubs Grasshoppers Zurich and St Gallen, Croatia's Hajduk Split, Kaiserslautern in Germany and local side Chernomorets Burgas.
The 49-year-old former Sporting Lisbon and Vfb Stuttgart playmaker was a key member of the Bulgarian team that finished fourth at the 1994 World Cup in the United States.
(Reporting by Angel Krasimirov; Editing by John O'Brien)
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