The 36-year-old Senegal international was sent off in the 13th minute following a confrontation with Keane, reducing Everton to 10 men for the majority of the match.
Despite the setback, the Merseyside club became the first team to win a Premier League game at Old Trafford after having a player sent off thanks to a superb 29th-minute goal by midfielder Kiernan Dewsbury-Hall.
Gueye will now serve a three-match suspension, missing upcoming league fixtures against Newcastle United, Bournemouth and Nottingham Forest.
"We have appealed and our appeal was turned down. We haven't been given any reason why it was turned down, but we did appeal it - immediately," Moyes told reporters ahead of Saturday's home game against Newcastle.
"It was over immediately. It was done, that was it. We moved on quite quickly and it was all sorted within the dressing room.
"We want passion. We don't always want it in the style it showed up on Monday night but we certainly want that passion and commitment from all the players."
It was only the third time in Premier League history that a player had been dismissed for a fracas with a teammate and the first time since 2008 when Stoke City's Ricardo Fuller slapped Andy Griffin during a match at West Ham United.
Moyes later said that Gueye had apologised and that the incident had some positives. Gueye also apologised for the incident in a social media post.
Everton are 11th in the standings with 18 points from 12 matches.