Not since the 1989-90 campaign, when Sir Alex Ferguson was reportedly one game away from the sack, have United lost four of their first seven league fixtures.
But Joachim Andersen’s first-half goal for Palace inflicted the same fate on the current crop, which left the Old Trafford faithful booing at the end.
Mount, who made his Premier League return after six weeks out with injury, says United must get better.
“We know we need to win these games and it’s been a difficult start,” the England international told the club’s website.
“As soon as they got the goal, they defended really well, they got bodies behind the ball and made it difficult to create. We had a few chances but it wasn’t enough.
“We know we need to go back and look at the areas that we need to improve on – and we need to improve because we want to win games, we want to win every competition we’re in, we want to go right to the end. So it’s a tough one to take.
“It was a tough start with the injury and a frustrating one but I used that time to look at areas where I could improve and coming back in the team last game, it felt good.
“But you don’t want to lose games and, especially at home with the fans, we want to perform for them and win games for them. And yeah, we need to improve. We need to go away and look at some areas that just weren’t there.
“But there are games coming thick and fast now. Every three days we’re playing in different competitions and this is a new start. The Champions League at home under the lights – it’s an exciting one to play in and hopefully we can perform and win that game now.”
Andersen’s brilliant goal – a sweet first-time finish at the back post from an Eberechi Eze set-piece – proved enough for Palace to earn revenge for their Carabao Cup defeat at Old Trafford earlier in the week.
And he enjoyed his match-winning moment.
“That goal, for me personally, is something I’ll remember,” Andersen told the club’s official website.
“It’s something that I need to improve on. I need to score more goals because I’m capable of scoring goals. I have the desire to score. I think I have a pretty good strike actually. I know I’m capable of scoring goals.
“It was a good cross from Ebs and I just felt that someone would get a touch and I just sensed where the ball would fall, like a good striker would do, and I hit it really well. Amazing goal.”