Lokomotiv went out at the last 32 stage after losing 4-3 in a penalty shootout following a goalless draw.
"After a meeting between Lokomotiv president Nikolay Gigov and Vasev the club decided that Vasev will go on leave until the New Year," Lokomotiv said in a statement.
"The club will offer him another post after that."
In April, former Bulgaria defender Vasev replaced Serbian Dragomir Okuka, who had been dispensed of in a similar fashion.
Vasev, 45, became the ninth coaching victim since the Bulgarian season started in August with changes also taking place at champions Litex Lovech and runners-up CSKA Sofia.
Europa League hopefuls Lokomotiv are fourth in the legaue standings with 25 points from 14 matches, nine points behind leaders Litex on 34.
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