The Brazilian player had to be stretchered off shortly after being brought on as a substitute in the 1-1 Europa League match against Fenerbahce.
Kobbie Mainoo, Leny Yoro, Harry Maguire, Luke Shaw, Tyrell Malacia and Mason Mount are also out of action.
Ten Hag is hopeful Jonny Evans will be back for Sunday's Premier League trip to West Ham, while captain Bruno Fernandes will be available again after being suspended for the game in Turkey.
But the United boss says injuries - which plagued the team's 2023/24 campaign - are a problem once more and the whole club must come together to find a solution.
Trending"Yeah, [the injuries] holds us back in our levels. And also in our position in the league," said Ten Hag.
"When you don't have the players available you can't line up the best team and that is what's holding us back in this moment and we need more players more often available.
"We have to work all together on this point, players, coaching staff, all the other staff we have to do better to get more available players. Because we know when we have them we are a really tough team to play and can be really successful, which is what we have shown over the last couple of months."
Ten Hag was unable to give an update on the severity of Antony's injury but said shared his concern for the winger, who left the stadium wearing a protective boot.
"It's really unlucky for him," Ten Hag told MUTV after Antony's fifth appearance of the season was cut short. "I feel real compassion for him, when he worked so hard in training.
"His training performances are that good that he deserved to come on. When you have to come off so quickly, that is really sad to see.
"Hopefully, it's not too bad, we have to wait 24 hours for what the assessment is."
Jose Mourinho was sent off during his side's draw with United on Thursday but was full of praise for his players after the match.
"They got a point against us, not us against them," Mourinho said. "We played amazing. If we play like this in the Turkish league we destroy everything because of course we played against a team with superior level than us. The Premier League has more quality, more intensity and more everything.
"I think my boys did an amazing match. Probably in England people will speak of two or three players for Manchester United who did not play, you do not know how many of us didn't play. At the start we had four players out of the list, and we had injuries. We had to do a crazy puzzle. Our performance was extraordinary. I could not ask any more from the players.
"Andre Onana made two fantastic saves. They scored in a situation we knew they could. We had a phenomenal performance.
"Come on, he saved the result. My goalkeeper didn't make a save, he made two impossible saves in 10 seconds. He was the most decisive player in the result. Of course he didn't make 20 saves but he made two that were incredible.
"I know English media will say Manchester United didn't play well but I think it would be fair to say we did an extraordinary match and we were better than them. A good result for Manchester United."
On the sending off incident, Mourinho told TNT: "I watched the incident. I don't want to speak about it."
On going to see the referee, Mourinho added: "He told me something incredible. At the same time, he could see the action in the box and my behaviour on the touchline.
"I congratulate him because he's absolutely incredible.
"During the game, at 100 miles per hour, he had one eye on the penalty situation, and he had one eye on the bench and on my behaviour.
"That's the explanation he gave me. That's why he is one of the best referees in the world."