Lokomotiv, who had Yordan Apostolov sent off in the 53rd minute, reached the quarter-finals for the second straight year thanks to Ivan Penev's precise fourth-minute header.
"Whatever I say, it will not be enough," Ludogorets coach Eduard Eranosyan told reporters. "It's shameful."
Ludogorets, who have won four consecutive league titles, two national cups and two domestic Supercups since 2011, became the second top-flight club eliminated by a second tier team this week after Botev Plovdiv lost 1-0 at Sozopol on Tuesday.
(Reporting by Angel Krasimirov; editing by Ken Ferris)
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