The Belgian international, who is on loan from Premier League champions Chelsea, wrote on Twitter that he heard “monkey noises” from the Atalanta supporters.
He wrote: “2018 and still racists monkey noises in the stands… really?! Hope you have fun watching the rest of @EuropaLeague on TV while we are through… #SayNoToRacism. #GoWatchBlackPanther.”
Atalanta were given a one-match stand closure last month, suspended for a year, after Napoli defender Kalidou Koulibaly was subjected to racist abuse.
Atalanta president Antonio Percassi later apologised to the Dortmund striker.
“I’ll be honest, I didn’t hear them. If they did happen, then I am very sad and absolutely apologise to Batshuayi. This should never happen,” said Percassi.
German side Dortmund grabbed a 1-1 second-leg draw through a late equaliser from Marcel Schmelzer to progress to the last 16 with a 4-3 aggregate victory, after the 24-year-old Batshuayi had scored twice in the opening game.