Liverpool coach John Achterberg and Newcastle's Daniel Hodges have been charged by the Football Association after an incident during the Reds' 2-1 win on 31 August.
The pair have been charged with improper behaviour.
Achterberg, Liverpool's goalkeeping coach, is also alleged to have used abusive and/or insulting gestures.
Hodges is Newcastle's head of performance.
Both have until 8 September to respond to the charge.
It follows a review by the FA into incident where a Newcastle staff member appeared to throw an object towards the Liverpool technical area.
Newcastle boss Eddie Howe called the late winner a "sickener" after his side had led 1-0 through a debut goal from £60m record signing Alexander Isak.