With United facing an intense schedule, United boss Ten Hag is eager to ensure that the player is managed correctly, given the raft of games in which they may need to be called upon.
United already have a significant amount of injury issues to contend with and the Dutch manager is eager to ensure that further key members of his squad remain fit.
Rasmus Hojlund was named on the bench for the clash in Turkiye and came on in the 55th minute as he replaced Joshua Zirkzee, who had laid on the assist for Eriksen's opener.
Hojlund missed the start of the season because of a hamstring injury but has now gone on to feature in seven games during the campaign.
Ten Hag wants to ensure that Hojlund, who has scored twice this season, remains fit.
Paul Scholes argued that Hojlund should have started against Fenerbahce along with Casemiro as United need to win games now to ease the pressure on the manager.
Speaking on TNT Sports, Scholes said: ‘I think if he played Hojlund and Casemiro tonight they would have made a big difference.
‘I know there’s games coming up but Erik ten Hag needs to win games now so play your best players.’
Hargreaves admitted that he agreed with Scholes but explained why he feels Hojlund was left out of the starting lineup.
Hargreaves said: ‘I think I’d have to agree. He [Ten Hag] is worried about Hojlund and his minutes, he knows he needs him for West Ham at the weekend.
Rasmus Hojlund, who missed the start of the season with injury, featured as a substitute
‘I definitely would have played Casemiro. [Manuel] Ugarte played really well, he looked good, but offensively United didn’t show much.
‘It was a fair result in the end. I don’t think United can expect to go there and win right now, given their form. But three points after three [Europa League] games isn’t good enough, clearly.’
Ten Hag's side have drawn all three of their Europa League games so far this season, with this game following on from stalemates against Porto and Twente.
United, who are currently in 12th place in the Premier League, return to domestic action away to West Ham on Sunday and then host Leicester in the Carabao Cup.
Antony left the stadium of crutches after suffering an injury against Fenerbahce. Kobbie Mainoo, Harry Maguire and Leny Yoro are amongst the other United players that are currently sidelined.