PSV goalkeeper Jeroen Zoet's misplaced clearance on the hour handed Ludogorets the opening goal in Eindhoven.
Zoet rushed out of his area to clear a long ball but found only Roman Bezjak who stroked it back past him into the empty net.
Former Netherlands midfielder Cocu said he had not underestimated the Bulgarians.
"We knew that Ludogorets could play well and would aggressively defend. They are also a team who can create opportunities," he said.
Ludogorets, who won their maiden league title last year and then retained their crown, were competing in the domestic third division only three years ago.
Coach Stoicho Stoev hailed a victory he described as "a historic moment for us.
"We came to Eindhoven with a lot to offer," he said. "But we did not expect to win."
In other matches, Spaniard Jonatan Soriano hit a hat-trick for FC Salzburg as the Austrian league leaders thumped Sweden's Elfsborg 4-0 in Group C.
Substitute Kevin Gameiro's goal lifted twice UEFA Cup winners Sevilla to a 2-1 win at Estoril in Group H and a second-half goal from Brazilian Hernanes secured Lazio three points with a 1-0 home victory over Legia Warsaw in Group J.
Fiorentina eased to a 3-0 win at home to Pacos Ferreira in Group E and Rubin Kazan romped to a 5-2 Group D victory over Maribor in Slovenia.