Referee Graham Salisbury and assistants Barry Gordon and Keith Lawson handed coins to the police, which had been thrown by home fans from the North Stand at Hillsborough, where the Owls lost 3-1.
A club statement read: "The referee, as a matter of course, noted the throwing of coins in his match report to the FA. This in turn means that the FA will investigate this very serious matter and the club could face a charge as a result.
"The throwing of coins and other objects is completely unacceptable and will not be tolerated.
"The club is currently in the process of reviewing CCTV footage to identify those responsible and condemns such behaviour. SWFC are working in conjunction with the Police to ensure that the culprits are both identified and made culpable for their actions."
Prior to kick-off both sets of fans had impeccably observed a minute's silence in memory of those who died at the Hillsborough disaster in 1989 and two soldiers from the Yorkshire Regiment who were killed last week in Afghanistan.
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