Koschitzke appeared to catch Elliott high with an elbow at the 24-minute mark of the second quarter.
The force of the contact sent Elliott to the ground, and he had to be helped to the interchange bench by trainers. Elliott returned to the ground early in the third term and played out the remainder of the game.
Shortly after the incident, Beams tweeted: "Fairly weak that by Justin Koschitzke #Cyalater."
The tweet was subsequently deleted.
Collingwood coach Nathan Buckley refused to comment on the incident after the game.
"I saw it very quickly during the play in the second quarter," Buckley said.
"The last time I was in this room and commented on a tribunal appearance (regarding North Melbourne's Lindsay Thomas in round one) it was made a bigger story than it needed to be, so we'll just let the powers-that-be deal with that."
Saints coach Scott Watters was also tight-lipped after the match.
"I actually haven't seen it so I can't comment on that one," Watters said.
"I thought [Koschitzke] competed hard, missed a couple of set shots. But again I need to really analyse that in the cold light of day."
Koschitzke was not reported by the umpires during Friday's match, but the incident is almost certain to be scrutinised by the match review panel.
If charged, Koschitzke will have points loading for a bad existing record, having been suspended for one match for striking Fremantle’s Zac Dawson in round four last season.
Dayne Beams' tweet before it was deleted on Friday night:
