A banner reading 'White Lives Matter Burnley' flew over Etihad Stadium on Monday when Manchester City faced Burnley.
Burnley have issued a strongly-worded condemnation after the offensive banner was towed by a plane above the stadium.
The incident occurred shortly after kick-off at the Etihad Stadium and it is still unknown who is behind that idea.
In a statement released at half-time, Burnley said: "Burnley Football Club strongly condemns the actions of those responsible for the aircraft and offensive banner that flew over the Etihad Stadium on Monday evening.
"We wish to make it clear that those responsible are not welcome at Turf Moor.
"This, in no way, represents what Burnley Football Club stands for and we will work fully with the authorities to identify those responsible and issue lifetime bans.
"We are fully behind the Premier League's Black Lives Matter initiative and, in line with all other Premier League games undertaken since Project Restart, our players and football staff willingly took the knee at kick-off at Manchester City.
"We apologise unreservedly to the Premier League, to Manchester City and to all those helping to promote Black Lives Matter."
Both teams players were wearing ‘Black Lives Matter’ on the back of their shirts, as has been customary since the Premier League return amid anti-racism protests.
Burnley captain Ben Mee also expressed his disappointment with those who initiated the idea saying: "I'm ashamed and embarrassed that a small number of our fans have decided to put that around the stadium."
"These people need to come into the 21st century and educate themselves. It does not represent what we're about, the club's about, the players are about and what the majority of the fans are about.
"It's a small minority of people and I'm really upset that has happened."