The matters relate to Palace's 1-0 defeat at home to Tottenham on 18 August in their first game since returning to the Premier League.
An Independent Regulatory Commission hearing held on 28 August found that the Palace boss had breached the rules and, after considering the written evidence, Holloway has decided not to lodge an appeal against the ruling.
"In relation to a breach of FA Rule E3 in that Holloway's language and/or behaviour in or around the match officials' changing room after the game amounted to improper conduct, he was given a two-match touchline ban to commence with immediate effect and fined £10,000," the FA said on their official website.
"In relation to a breach of FA Rule E3 in that Holloway's post-match comments constituted improper conduct in that they questioned the integrity of the match referee and/or match officials in general, and/or implied that the match referee and/or match officials in general were motivated by bias; and/or brought the game into disrepute, Holloway was fined £8,000."
Holloway will now be banned from the touchline for Palace's trip to Old Trafford to face Manchester United on 14 September, and will complete his ban when Swansea come to Selhurst Park a week later.