The phrase "admit that the problem" is correct and usable in written English.
You can use it when acknowledging or confessing the existence of a problem in a discussion or argument.
Example: "During the meeting, she had to admit that the problem with the project was due to a lack of communication among team members."
Alternatives: "acknowledge that the issue" or "confess that the difficulty".
We need to admit that the problem is real.
But even the Labour leader had to admit that the problem goes beyond one party or one government.
Because of who he is, John Lindsay just can't admit that the problem of providing decent health care to the South Bronx is impossible for him to solve.
Senor does admit that the problem may have been more acute on the right-wing side, but then says that it wasn't just on that side, because Rasmussen got it wrong.
Though she has written a book on the subject and was, for a time, head of the International Anticounterfeiting Coalition, Ms. Kolsun is the first to admit that the problem is bigger than she is (5 feet 1 inch).
It's much easier to blame environmental standards, planning bodies and pro-planning groups that try to protect our collective quality of life than to admit that the problem is either largely one's own fault or beyond one's control.
School principals themselves admit that the problems with that approach are many.
Indeed, at the congressional hearings, the tech companies admitted that the problem was far larger than they had originally said.
It began providing daily updates on case numbers and admitted that the problem in China was indeed related to the SARS epidemic elsewhere.
He called the first year of his drug war "a fiasco" and admitted that the problem would persist beyond his tenure.
Pope Pius XII, in 1950, was far more prudent; he claimed that the tomb of the first Apostle had been found, but he admitted that the problem of identifying the actual bones was close to insoluble.
