Bristol City manager Sean O'Driscoll said that although the match against Bristol Rovers was "tremendous", violence which broke out after the football derby was "disgraceful".
Mr O'Driscoll added: "That's what people will now be talking about...players were disappointed as well. The game was played in good spirit, competitive but not overzealous. We wanted the supporters to act in the same manner but unfortunately they didn't".
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Police are trying to find the driver of the car following the incident in Kingfisher Close, Brownhills.
An unnamed man died at the scene, while a woman was pronounced dead after being taken to St George's Hospital, Tooting, south-west London.
Eastern areas will see a few showers coming in on the northeasterly breeze