The club tried to get FA officials to review the incident on video, but the officials decision was upheld and the sending off will stand.
"We received an appeal from the club and sent the video to the Video Advisory Panel," said an FA spokesman.
"The appeal has failed and the player will now serve a three match suspension, starting on March 12."
Davis will now miss the home game with Southampton on March 15th, the away game at Manchester United on March 22nd, and the home game with Blackburn on April 7th.
