The phrase "admitted not only" is correct and usable in written English.
It can be used when you want to express that someone has acknowledged or confessed to multiple things or aspects, typically followed by "but also" to introduce additional information.
Example: "She admitted not only her mistake in the project but also her lack of preparation for the presentation."
Alternatives: "acknowledged not just" or "confessed not only".
He admitted not only to stealing bone and tissue samples from numerous corpses, but also to forging consent forms and medical records so that processing companies would accept the samples.
Greece had admitted not only that the cost of mounting the Olympic Games in August had pushed its annual budget deficit beyond the 3% cap every year since 2000 but also that it had used inaccurate earlier numbers in order to be admitted to the EMU in 2001.
Anthony Hathaway identified himself, handed over $2,310, and admitted not only to that bank holdup, but to 29 others, officials said.
Compared with the previous two studies, a much larger number of number of patients were enrolled in the present study (n = 1440), and they were admitted not only to the medical ICU but also to the surgical ICU at multiple centers.
Founded at a time when Egypt was occupied by the British, the club was unusual for admitting not only Jews but Egyptians.
The minute the drugs kick in, the façade drops and he admits not only fear at becoming a father, but hostility toward his unborn.
Even the "spiritual but not religious" set might be intrigued by a pope who, by resigning his position, admits not only his own frailty but that of the throne on which he has been seated.
Soon, however, Maupin recanted, admitting not only that the book was the next "Tales" installment, but that he had yet another still in mind. Et voilà: the tenderhearted and frolicsome "Mary Ann in Autumn".
An honest assessment of Ives should admit not only that he had a bent for tall tales but that his obscurity in the first part of the century was largely a result of his disdain for the music business.
Landis went as far as writing his own book protesting his innocence, but abruptly changed his story last May, admitting not only that he had doped, but accusing Armstrong of doing so, too.
If it happens, the official stressed, Rose will have to apologize for lying for 13 years and to admit not only to his baseball gambling but also to other transgressions.
