The injury-hit Red Devils suffered a club-record 13th defeat of a Premier League campaign on Monday, losing 4-0 at Crystal Palace.
The club are languishing in eighth place in the table ahead of Sunday's daunting clash against title-chasing Arsenal, then have two further league games before attention turns to the FA Cup final.
The May 25 meeting with Manchester City offers the chance to end a poor season on a high, but FA Cup success was not enough to save compatriot Louis van Gaal's job in 2016.
Asked if he was concerned that he could be sacked even if he won the FA Cup, Ten Hag said: "No, I think they have common sense.
"They see when you have 32 different backlines, when you lose eight centre-backs, if they see we use 13 partnerships at centre-halves.
"When they see we don't have a left full-back, when we have so many injuries, they know that will have a negative impact on results."
The Dutchman said United were "still fighting" and the FA Cup final could yet be a highlight of the season, even though City will be overwhelming favourites to win at Wembley.
"Of course we are not happy, but we know the reasons why we are underperforming in the ranking now and that is because of the injuries," he said.
"I am a realistic person and I see this when I make this analysis and no team will perform when you have so many injuries in key areas."
New United co-owner Jim Ratcliffe has made sweeping changes to the club hierarchy since arriving at Old Trafford earlier this year but there has been no official verdict on Ten Hag's future.
Ten Hag brushed aside suggestions that it would be beneficial for Ratcliffe and his INEOS group to publicly confirm he would continue next season, saying it is a "question you have to make to the owners, not to me".
Marcus Rashford, Scott McTominay and Bruno Fernandes have returned to training ahead of the Arsenal clash, but Mason Mount and Luke Shaw are dealing with setbacks.
Asked whether anybody is definitely out of the FA Cup final, he said: "Not in this moment, definitely, but we have some doubts.
"We have some players really fighting to be available and that is so amazing. They all try, they are all desperate to play.
"Yesterday, Licha (Lisandro Martinez) came to me and he wanted to play on Sunday against Arsenal, but he's not ready yet. He needs a little bit more time to go through the process.
"But he's so desperate and there are more -- Rapha Varane, Victor Lindelof.
"Luke Shaw had a setback in his process as well, but there's still a hope and he will fight to be available for the final."
