Martinez was injured in the second half of United's 3-0 victory over West Ham last weekend, but controversy surrounded Ten Hag's failure to immediately replace the centre-back.
When Martinez was initially injured, he received treatment then briefly carried on playing before breaking down again and finally coming off.
The 26-year-old's ligament damage in his right knee will sideline him for a significant period, but Ten Hag said injury substitutions can be a "grey area".
Asked if carrying on had aggravated Martinez's injury, leading to a longer spell out of action, Ten Hag told reporters on Thursday: "I don't think so, but it was his decision.
"He was comfortable to be back on the pitch but after he tried and then I think stopped in the next attack.
"In some situations it is clear and obvious but there is always a grey area and it's very difficult to see when you are on the sideline.
"We have the screens and we see it as well, and our medics are over there and they are communicating with the player, but to assess in one or two minutes is impossible.
"You need 24 hours minimum and sometimes even longer, so how can you do this in two minutes?"
It was only Martinez's fourth game back following a lengthy spell out because of a recurrence of a foot issue, with United winning three of those matches and drawing one.
"It is a big setback, of course. Licha was returning, you see his contribution to the team when he is playing, apart from the technical skills also the mentality," Ten Hag said.
"He is very disappointed about it but he is a fighter. He will be back stronger and we think he'll be back by the end of the season.
"As a squad, we have to replace him and we have very good players in that position who can play there."
Raphael Varane replaced Martinez while Victor Lindelof and Jonny Evans are also options for Ten Hag in Sunday's trip to Aston Villa.
Beating fourth-placed Villa would be a major boost to United's hopes of qualifying for the Champions League.
They go into the clash eight points behind Villa but Unai Emery's team have won only one of their last five matches and were knocked out of the FA Cup by Chelsea on Wednesday.
"I've said to the team from the start of January, every game is now a final," Ten Hag said.
"That was also our approach to West Ham. We were one point behind them but this is a final, we have to take this challenge, we have to see this as a final. That will be every game from now on so we are already in that mood."
