The Red Devils slipped to fourth on the table, falling eleven points behind the leaders.
Things started brightly for the visitors at the Emirates Stadium when Marcus Rashford gave them a 17th minute lead but Eddie Nketiah and Bukayo Saka turned the game around for the hosts before Lisandro Martinez brought them level again.
Nketiah's second of the day in the 90th minute gave Arsenal the win which saw United drop late points for the second successive game.
Ten Hag opined all three goals United conceded were avoidable and has tasked them to improve.
"I think two games head to head, really close, it's hard to accept that in the end you lose in the final stage of the game," Ten Hag said.
"It can't happen, and we have to accept that, we have to learn the lessons. All the three goals, we could and we had to avoid them. Normally we are better in such situations."
"We started the game very well and scored the goal and were leading, and then made mistakes that were unacceptable," Ten Hag added on Sky Sports.
"We have to learn the lessons and move on.
"We will face the players with this because it can't happen. Good players don't make such mistakes."
Asked if the result might serve as a reality check, Ten Hag said: "It can be. Today we have to accept we are unsatisfied with this defending performance because we can do better.
"We went up 1-0 and the game is starting very well. Then you have to take benefit from that situation, and it can't happen that we concede a goal like we did.
"This is one game. Last week we did very well and kept the opponent away from our own box. If we were in the box we defended much better. Normally we don't concede goals from corners, and today there were two."
