Monday's 4-0 defeat by Crystal Palace at Selhurst Park leaves United eighth in the Premier League, with Arsenal to come at Old Trafford on Sunday.
Manchester City await United in the FA Cup final at Wembley on 25 May, when the club could salvage their season with victory against their rivals.
But, despite the club sacking Louis van Gaal in 2016 after he won the FA Cup, Ten Hag says the owners "see the reasons" behind his side's performances this season.
"I think they have common sense," said Ten Hag.
"They can see when you have 32 different backlines, when you lose eight centre-backs, when they see us use 13 different partnerships at centre-half, when we don't have a left-back, when we have so many injuries - that will have a negative impact on results."
Ten Hag said he was "not happy" with results this season, but that he has to be "realistic" given the injuries in his squad.
Sir Jim Ratcliffe acquired a 27.7% stake in the club in January, which has given the 71-year-old full control of football operations at Old Trafford.
Ten Hag says he does not need a public vote of confidence from the board, despite speculation over his future.
"I don't care if they do or they don't, I'm working on improving and developing my team, that is my job here," Ten Hag added.
-- Courtesy of BBC Sport