The incident led to Gueye's dismissal for violent conduct, resulting in a three-match ban.
Despite playing with 10 men for over 80 minutes, including stoppage time, Everton secured a 1-0 victory against Manchester United.
Gueye issued a public apology on social media, taking full responsibility for his actions and expressing regret to Keane, his team-mates, staff, fans, and the club.
Everton manager David Moyes confirmed Gueye had apologised privately to Keane and questioned the referee's swift decision to issue a red card.