In a statement the club 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.
The club has a proud record of working with all genders, religions and faiths through its award-winning Community scheme, and stands against racism of any kind.
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.
Burnley captain Ben Mee also joined the condemnation.
He said he felt “ashamed” and “embarrassed” by the stunt from a “small number of fans”.
“I’m ashamed and embarrassed that a small number of our fans have decided to put that around the stadium,” said Mee.
“They have completely missed the point and there’s a group of lads in there who are embarrassed to see that.
“It’s not what we are about at all and has missed the whole point of what we’ve achieved and what we’re trying to do (through backing the Black Lives Movement).
“These people need to educate themselves – as a lot of us do – and, like I said, it completely missed the point of the whole thing we’re trying to achieve.
“It does not represent what we’re about, the club’s about, the players are about and what the majority of fans are about, I’m sure. It’s a small minority of people and I’m really upset that happened.
“I’m ashamed and upset it’s associated with our club – my club – and it’s not something we want to see at all in the game. We totally condemn it and are embarrassed by it.”
Former Manchester City player and Sky Sports pundit Micah Richards also said the banner was “so disheartening”.
“After how far we’ve come in this last couple of weeks, it really does hurt me,” he said.
“Just at a time when things looked on the up, you’ve always got a small fraction – it’s not everyone – who just want to spoil things. But I don’t want to make a massive thing of that when we’ve got something so positive going on.”
Burnley’s players and coaching staff had joined Manchester City in taking a knee as their match kicked off, becoming the 20th Premier League club to show support for the Black Lives Matter movement.
Since the Premier League resumed on 17 June after a three-month break because of the coronavirus pandemic, all players have taken a knee before kick-off and have worn “Black Lives Matter” on their shirts.
It is a show of support for racial equality following widespread protests over the death of George Floyd, an unarmed black man, while in police custody in Minneapolis.
Kick It Out, English football’s anti-racism charity, said the sentiments of the banner flown over the Burnley game represented a grave misunderstanding of the Black Lives Matter initiative, reports Sky News.
The organisation’s chairman Sanjay Bhandari said: “The point of Black Lives Matter is not to diminish the importance of other people’s lives.
“It is to highlight that black people are being denied certain human rights simply by virtue of the colour of their skin.
“It is about equality. We shall continue to support the Black Lives Matter movement and the fight for greater equality for all in football.”