The end of Middlesbrough vs Manchester United game was marred by ugly scenes following United's 3-1 win at Riverside stadium.
Gestede initially appeared to bite defender Eric Bailly in a stoppage time melee on the edge of the visitors' area in an altercation missed by referee Jon Moss and his assistants.
Replays showed there was no contact as the pair engaged in an angry clinch, but punches appeared to be thrown.
However, after the final whistle, as players from both sides made their way off the field, the verbals began once again.
Depending on the officials' report, the FA could be called to act following the ugly scenes.