United conceded twice deep into stoppage time as Chelsea sealed a dramatic 4-3 win at Stamford Bridge on Thursday.
The Red Devils, who sit sixth in the Premier League table, also conceded a 99th-minute leveller at Brentford on Saturday.
They are currently nine points adrift of fifth-placed Tottenham with eight matches remaining and 11 points behind fourth-placed Aston Villa, who have played a game more.
With league leaders Liverpool next up at Old Trafford on Sunday, United boss Ten Hag acknowledged it will be “difficult” to bridge the gap to the teams above them.
Fourth place will guarantee entry into the Champions League next season and the team finishing fifth could also qualify, based on the record of Premier League clubs in European competitions this season.
“This week we’ve dropped points in stoppage time,” Ten Hag said.
“We’ve dropped five points and that’s very expensive because the points are getting more expensive because the games are running out. We know that and we have to catch up.
“We are many points behind. It will be difficult but we will keep fighting and our team has character.
“We have seen (against Chelsea) they are resilient and we will be in the fight against Liverpool.”
When asked if United will need to produce a flawless end to the season to make the top four, he added: “Yes, but that is also what I said before (the Chelsea) match.
“I have to manage the team. We have qualities, some great players, we can play to a very high standard.”
The Dutch manager also noted the importance of United supporters avoiding tragedy chants about the 1989 Hillsborough disaster for their meeting with Liverpool this weekend.
“It’s very important to be behind Manchester United and to support us in a positive way,” he said.
“There is a fantastic bond between the team and the fans and we want a positive mood at Old Trafford on Sunday.”
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