Both incidents happened in last Sunday's Old Firm game
Thursday 4 April 2019 20:59, UK
Rangers manager Steven Gerrard has accepted a one-match ban, while forward Ryan Kent has lost his appeal and will miss two games.
Kent had contested the Scottish FA's charge for appearing to strike Celtic captain Scott Brown, and on Thursday morning, Gerrard and Brown were charged by the SFA for separate incidents.
Gerrard's charge was based on comments made to referee Bobby Madden in the aftermath of Rangers' defeat at Celtic Park.
Kent - on loan from Liverpool - scored a 63rd-minute equaliser for 10-man Rangers after striker Alfredo Morelos was sent off in the first half.
However, after Celtic's James Forrest scored the winner in the 86th minute, Kent approached Brown and shoved him, leaving the midfielder on the ground.
He was alleged to have breached Disciplinary Rule 200, whereby "any one of the sending off offences of (A1) serious foul play, (A2) violent conduct, and (A3) spitting at an opponent or other person is committed by a player at a match, but that sending off offence was not seen by any of the match officials at the time that it was committed."
By contesting the SFA's charge, Kent was able to play in Rangers' 3-0 win over Hearts on Wednesday, but the lost appeal means he will miss an away game against Motherwell followed by the first fixture after the Scottish Premiership split.
The team will already be without Morelos, who has three games remaining of his four-game suspension.
Meanwhile, Gerrard was charged with Disciplinary Rule 203 - "No member of Team Staff shall commit Misconduct at a match" and will also be absent from the dugout when Rangers head to Fir Park to face Motherwell on Sunday.
Gerrard's side are 13 points behind league-leaders Celtic, who could secure an eighth consecutive title if they beat Livingston and Rangers lose.