Uefa levelled the English Football Association with four charges, including a pitch invasion and the lighting of flares by supporters inside the ground.
The national lead for policing, Cheshire Police chief constable Mark Roberts, now wants Football Banning Orders imposed for drug possession.
He said cocaine has been a problem substance in stadiums for years and its use was ‘prevalent’.
Banning orders can be given in relation to alcohol misuse, for offences including ‘possession of alcohol or being drunk while entering/trying to enter a ground’, but not drugs.
Mr Roberts told the Independent: ‘We would very much like to bring that up to date with drug usage and make that a trigger in the same way.’
Anyone subject to a banning order who breaks it can receive up to six months in prison, a £10,000 fine or both.
University of Kent anthropologist Dr Martha Newson suggested cocaine may have given drunk fans the energy to storm Wembley.
She said: ‘To sustain a day of drinking and still have the energy and coordination to push through security late in the day would be unusual.
‘For a decade or more, many hardcore fans have used cocaine to maintain their energy in a way that alcohol cannot. Cocaine use is yet to be addressed in football.’
A Home Office spokesperson said: ‘Football-related violence and disorder of any kind will not be tolerated, which is why around 1,400 hooligans are currently barred from attending games under Football Banning Orders.
‘The legislation is kept under constant review and this week the prime minister announced it would be extended so online abusers can be banned from stadiums for up to 10 years.
‘Drugs devastate lives, ruin families and damage communities, which is why we are setting up a new cross-government drugs unit to tackle the issue.’
MORE : Idiot drank 20 ciders, snorted coke, put flare up backside then stormed Wembley
MORE : Two men, 18, arrested for ‘helping ticketless mob storm Wembley’ at Euro final
MORE : Met says England match could have been called off as they deny failure over invasion
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