With 18 minutes remaining at Pittodrie and with the score at 1-1, the winger was given a straight red card for a challenge on defender Mikael Lustig.
A Scottish FA disciplinary tribunal reviewed the case and rejected the claim of wrongful dismissal.
Hayes will now serve a two-match suspension.
The appeal process meant the 28-year-old Irishman was free to play in Tuesday's 1-0 win over Hamilton, which took the Dons five points clear at the top of the Premiership.
However, he will miss Saturday's visit to Hearts and the following midweek League Cup meeting with Hibernian.
Speaking after the win against Celtic, Aberdeen manager Derek McInnes thought the red card was harsh.
"It's not a two-footed challenge," he told BBC Scotland. "If he [referee Craig Thomson] sees again, I'd be surprised if he thought it was a red card but it is what it is. We had to deal with it and we dealt with it."

The 26-year-old scored 20 goals in 52 games for Bristol City, after signing from French club Angers in July 2015.
The Ivory Coast international had also been the subject of interest from Derby County and Premier League side Hull.
Villa had reached an agreement to sign Hull forward Abel Hernandez, but the move fell through over personal terms.
Bristol City owner Steve Lansdown had previously said they would not sell Kodjia to any fellow Championship club, and that any deal would have to exceed £10m.
The deal represents the largest transfer fee City have ever received for a player, surpassing the £3.5m the club sold Ade Akinbiyi to Wolves for in September 1999.
Villa boss Roberto Di Matteo said he had signed a "proven goalscorer" in Kodjia, while City chief operating officer Mark Ashton said the club had retained a sell-on clause and decided to disclose the fee "due to the high-profile nature and speculation surrounding the deal".
Ashton added: "We've continually told Jonathan that we don't want him to go, but recently he's made it clear that he's aware of the interest of other clubs and that he wanted to leave."
Kodjia is a proven goal scorer at Championship level, a physical and competitive style of player with greater mobility than a Rudy Gestede or Libor Kozak.
Whether he is quite the "world-class striker" that Villa chairman Dr Tony Xia promised via his prolific Twitter account is dubious, but he could well thrive on the sort of service Ross McCormack and Jack Grealish are capable of providing.
The Villa squad was always going to need revolution rather than evolution after last season's psychologically damaging relegation - Kodjia is the latest component of a summer of change.
Aberdeen have been unsuccessful with their appeal against Jonny Hayes' sending off in Saturday's 2-1 victory over Celtic.
[NEXT_CONCEPT]
Aston Villa have signed Bristol City striker Jonathan Kodjia on a four-year deal, for an initial £11m that may rise to a Championship record fee of £15m.