An early goal by Erling Haaland, scored within the opening minutes, secured the victory for City and gave them a crucial lead.
It is Burnley’s third relegation in their last three top-flight seasons and their fifth Premier League relegation overall, second only to Norwich City’s six.
Wolves had already had their relegation confirmed, meaning only one spot remains to be decided. Tottenham currently occupies the final relegation place.
Relegation to the second tier had been inevitable for Scott Parker’s side, who have only won just one of their last 25 league games. Defeat to Man City at Turf Moor also extended Burnley’s winless home run to 13 league games.
“We’ve had an understanding that the inevitable was getting closer,” Parker told Sky Sports. “That curtain has come down on us now, the confirmation has been there. We’ve failed and come a little bit short today.
“I can’t be critical of this team. This team have given us everything every single day. You can fault us in certain moments where we lacked a quality about us — and we haven’t got enough points in this division. I think tonight’s performance represents us a little bit of what we are.
“I’m immensely proud of this team. I may get ridiculed for saying that in the world we live in. I’m being honest, but that’s the way it is.
“These players have come in with a humongous challenge and we’ve fallen a little bit short. We needed to overachieve this year. Overachieve and overachieve, every single game. And we haven’t managed to do that.”
Parker declined to give a definitive answer about his own future and whether he would be the coach to try to lead Burnley back to the Premier League once more.
“Regarding myself, like always, we’ve given everything, sacrificed a lot of things and we’ve fallen short.” he said.
“I hold the burden for that and the responsibility for that. We’ll keep moving and keep going.
“Fundamentally now, the most important thing is reflecting on this season. Everyone at the football club, work out the way forward and go from there.”