A selection of the Derby fans could allegedly be heard singing, "You're going down with your chairman, where's your chairman gone," during Derby's 1-0 win over Forest last night, which is a reference to the sudden death of Forest chairman Doughty.
Glick told the club's official website: "We are very disappointed that a brief moment of insensitive and distasteful chanting by a minority of supporters spoiled what was a great occasion at Pride Park Stadium last night and we do not condone the actions of those individuals in any way, shape or form.
"The vast majority of our supporters come to Pride Park to enjoy watching and cheering the Rams on to victory and generate a positive atmosphere inside the stadium.
"It is a shame for this majority that we today have to focus on a small group of people whose actions reflect badly on us all."
The club have confirmed that they will undertake a review of the incident from last night's Championship match.