Liverpool fans watched their side fall apart in the second half on Wednesday night
The charges laid against Liverpool are for crowd disturbances and the setting off of fireworks, and Sevilla for crowd disturbances and the throwing of objects.
Unai Emery's side won 3-1 on the night after a stunning second-half turnaround.
Jurgen Klopp's team are now without any European football next season.
Victory would have secured a place in the Champions League, but fans at Anfield will have to wait at least another year before they welcome European opposition again to Merseyside.
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