Phil Neville has called on Chelsea to sack assistant coach Marco Ianni for his role in the unsavoury scenes which followed the Blues' late equaliser against Manchester United.
United manager Jose Mourinho was peeved at the way Ianni celebrated Ross Barkley's injury-time strike, prompting a melee around the tunnel.
The Portuguese received an apology from Ianni and Chelsea manager Maurizio Sarri and said he considers the matter closed, but former United full-back Neville thinks the west Londoners should contemplate further action.
The England Women manager said on NBC Sports: "Whoever that staff member is of Chelsea has just been an absolute disgrace. No class, no humility.
"He's gone straight into the face of Jose Mourinho, Michael Carrick and the Manchester United bench and just celebrated in their face. Absolutely disgraceful.
"He's [Mourinho] the innocent one in all this. The guy on the Chelsea bench has run straight past him, celebrated in his face.
"Sarri celebrates. Then it's this guy here who goes in front of Jose Mourinho. The first one he clenches his fist, and then as he goes back he celebrates again right in front of him. Disgraceful.
"If I was Maurizio Sarri I'd send that guy in and sack him from the club."
Sarri also said he would speak to Ianni again on Sunday.
The Football Association is awaiting the referee's report before deciding whether any further action is warranted.
The issue overshadowed a pulsating 2-2 draw, in which United hit back from Antonio Rudiger's first-half goal thanks to Anthony Martial's brace after the interval, only for Barkley to seal a share of the points late on.