Roy Hodgson's side inflicted a fifth defeat of the season on United, prompting a loud negative reaction from the home fans.
"I understand," said the Man United manager afterwards.
"When we play at home or away and we play Crystal Palace, we have to win. With all respect, I know every game in the Premier League is very difficult, you have to play your best and I understand fans expecting a win and we didn't win, we lost."
It's the first time since 1989 that United have lost four of their first seven league games. It leaves Ten Hag's team 10th in the table and the Dutchman said there could be "no excuses" for the poor start to the campaign.
"We have to be more consistent," said Ten Hag.
"The demand is we get a row of wins and we have to do better than we do now. I can give you reasons but you will explain it as an excuse and there are no excuses, we need to win."
Meanwhile, Palace's 76-year-old manager Hodgson was left to celebrate extending his unbeaten run at Old Trafford to five games; four with Palace and one with Watford.
"I am happy about that [record] but what I am most happy about is the way the team played, and so pleased for the players," added Hodgson, whose team lost 3-0 at home to United in the Carabao Cup on Tuesday.
"It's not easy coming here for the second time in a few days and give that performance and work so hard for 90 minutes."