The Football Association is reviewing an incident where a Newcastle staff member appeared to throw an object towards the Liverpool technical area during the Reds' 2-1 win on Wednesday.
It is unclear if the incident, captured on television, sparked the melee in front of the dugouts.
Newcastle declined to comment when contacted by BBC Sport.
Referee Andre Marriner added on five additional minutes, but several Newcastle players went down with cramp, while goalkeeper Nick Pope also suffered an injury during the extra time.
When asked about Newcastle's apparent time-wasting, Klopp said on BT Sport: "It's the perfect response to that.