Varane went off at half-time before Martinez was stretchered off in injury time. Sevilla scored two late goals as United imploded during the last 10 minutes and Ten Hag is facing selection problems for the trip to Nottingham Forest on Sunday with Marcus Rashford, Luke Shaw, Scott McTominay, Alejandro Garnacho and Donny van de Beek already sidelined.
Martinez looked in a lot of discomfort as he left the pitch, although Ten Hag denied the Argentinian had torn his Achilles.
"It is not the area, I can't tell [what it is] but it is not the area of achilles," said Ten Hag.
"I think he will not play on Sunday. It looks like that but I can't say what the diagnosis is and I prefer to wait and say what it is. We have very good replacements with Harry Maguire, Victor Lindelof and Luke Shaw so we have players who can replace them [Martinez and Varane] but of course it is a miss."
United scored twice in the opening 20 minutes against Sevilla through Marcel Sabitzer as Ten Hag's team took control of the game.
But a sloppy second-half performance ended with both Tyrell Malacia and Maguire scoring calamitous own goals in the final six minutes to give the Spanish side the edge ahead of the second leg in Spain next week.
"I had to make them [the substitutions], there was no other way," said Ten Hag. "Rapha [Varane] was injured, I had to make [the change]. Anthony Martial, first start after a long period so we had to make it on 60 minutes.
"Then Bruno, I got the warnings from the refs he was short before his second booking and the same for Antony, so I had to make the subs, I had no choice.
"Both [Sevilla] goals are really unlucky, two deflected. What can you do? Sometimes you have bad days and bad luck. Tonight was not our night."