The controversial striker escaped punishment from referee Howard Webb for appearing to kick Tottenham Hotspur midfielder Scott Parker during City's 3-2 win over Spurs on Sunday.
Following the match, the Football Association reviewed tapes of the incident and decided to charge the 21-year-old with violent conduct.
"We are likely to be without a player for four games," said Platt. "We have not sat down as a group to discuss it.
"But I don't think anybody thought we would win an appeal with Vincent Kompany, even though the majority of people didn't feel he deserved a red card or a four-match ban. It shows the futility of an appeal sometimes. This looks poor when you slow it down."
City have until 6pm on Wednesday to appeal the suspension.