Shortly after Michael Keane had given Everton the lead, stewards struggled to stop a large section of Hajduk supporters from making their way onto the pitch, with video footage showing at least one punch thrown towards a steward.
The game was also delayed for several minutes while order was restored in the corner of the ground, and UEFA has acted quickly in determining charges for both clubs.
Hajduk are said to have committed four offences, which are the throwing of objects, crowd disturbance, field invasion by supporters and acts of damages.
Everton have been notified that they are being charged with the throwing of objects, with a date for an official hearing yet to be announced.
The home team eventually ran out 2-0 winners ahead of next week's second leg in Croatia.