Martinez faces at least two months out after sustaining medial collateral ligament damage in United’s win over West Ham, with the club hopeful he will recover from the knee issue before the end of the season.
It was only the 26-year-old’s third Premier League game back after returning from a foot injury that kept him out for more than three months.
Speaking ahead of his side’s trip to face Aston Villa this weekend, Ten Hag made it clear how much his side will miss Martinez.
“You see his contribution to the team when he is playing so he brings, apart from his technical skills, also a mentality in the team,” Ten Hag said.
“It is a big setback for Licha. He is very disappointed, but he is a fighter and he will back, he will be back stronger. We think he will still be back by the end of the season.”
After receiving treatment, Martinez briefly returned to the pitch against West Ham, but it swiftly became clear that he was unable to continue.
Ten Hag insisted it was the defender’s decision to try and play on, and denied the suggestion that the knee problem was aggravated.
“To assess in one or two minutes is impossible,” Ten Hag said.
“After a game I always tell you I can't tell [about the severity of injuries] because you need 24 hours minimum and maybe sometimes even longer. So how can you do this in two minutes?"
Harry Maguire, Victor Lindelof, Jonny Evans and Raphael Varane are all fit and could come into the side and replace Martinez, though Ten Hag also talked up the possibility of shifting Luke Shaw into the centre of defence, as he has done at times in the past.
"We have options, [for] how to deal with that position,” Ten Hag said.
“We have good centre-halves in our squad. The others are also available. Luke can play also there. So I am quite confident that we can keep this process going and that others can fulfil that position and contribute playing high levels.
“Those players are very experienced and are very good players, so it is up to them now to fulfil it."