"I heard rude abuse...racist ones," the Brazilian marksman was quoted as saying on Shakhtar's website (http://shakhtar.com/en/).
"Supporters behaved improperly and that is why I am disappointed and feel resentment. It was an ugly act from their side,” he added.
On a record-breaking night, Luiz Adriano became the first player in the history of the competition to score four goals in the first half.
He also joined Barcelona's Lionel Messi as the only players to hit five goals in a Champions League game.
Shakhtar's 6-0 halftime lead created a new mark for the competition and the margin of victory equalled the best away from home set by Olympique Marseille when they triumphed 7-0 at MSK Zilina in 2010.
Ukrainians Shakhtar are now second in Group H on five points, two behind leaders Porto who beat Athletic Bilbao 2-1.
BATE are third with three points from three matches while Bilbao have one.
Luiz Adriano scored in the 28th, 37th, 40th, 44th and 82nd minutes - two of his strikes coming from penalties.
"I am excited that my record helped the team. It was a beautiful and historic victory," he said. 

Latest News from Sports News Desk