Martial emerged as a doubt for the game when he was pictured limping during the warm-up, but he was able to take to the field for the first whistle, and the France international provided the assist for Antony to level the scores for the visitors.
The number nine had to be substituted in the 29th minute of the contest, though, with his replacement Cristiano Ronaldo going on to score the winner at Goodison Park.
Ten Hag has said that he is unsure of the seriousness of the issue at this stage, with a clearer picture likely to emerge in the coming hours.
“I have to see. I cannot tell what it is or how serious it is. Let’s wait for the first 24 hours and see how serious it is, then I can give an answer,” Ten Hag told reporters after the match.
In a separate interview with BT Sport, meanwhile, the Dutchman said that it was “something different” for the attacker rather than a recurrence of a previous issue.
“No I don’t think so [it is a recurring issue]. It’s something different. He had a problem in his back,” he said.
Martial was strongly linked with a move away from Man United earlier this year, and he finished last season on loan at Sevilla, who turned down the chance to sign him on a permanent deal.
The 26-year-old impressed Ten Hag during pre-season, though, and he had been in line to start the 2022-23 campaign in the team before picking up a hamstring problem.
Martial was also on the sidelines at the end of August and throughout September with an Achilles complaint before scoring twice off the bench against Manchester City in the league on October 2.
The attacker was also on the scoresheet as a second-half substitute against Omonia last week before starting against Everton, but he is now facing another period on the sidelines.
The Frenchman’s long-term future at Old Trafford is currently unclear, as his deal is due to expire in June 2024, although Man United have the option of activating another 12 months.
Since arriving in Manchester from Monaco in September 2015, Martial has represented the club on 273 occasions in all competitions, contributing 82 goals and 52 assists in the process.
The forward is now a major doubt for Man United’s Europa League contest with Omonia on Thursday night.
The Red Devils are currently preparing for three home games in quick succession, following the European clash with Premier League games against Newcastle United and Tottenham Hotspur.