The club are investigating the incident, with a tannoy announcement in the second half of the game at the John Smith's Stadium saying "racist chanting is affecting the game and will not be tolerated" after McClean was the target for abuse.
Cowley said: "The first I knew about it was when the referee spoke to us. We are still waiting for the referee's report.
"As a club and certainly from myself, there is absolutely no place in football or society for any discrimination at any level.
"It is always sad when it happens. Football is a brilliant game; a game I love dearly and it is horrible when situations like this arise.
"Unfortunately, I don't think it is just football, but a society issue and it is something we all have a responsibility as human beings to tackle together."
Meanwhile, Cowley remains hopeful of doing some incoming transfer business ahead of the weekend trip to Southampton in the FA Cup.