The phrase "acknowledge a degree" is correct and usable in written English.
You can use it when referring to recognizing or admitting the existence or importance of a certain level of something, such as knowledge, skill, or achievement.
Example: "In order to progress in your career, it is essential to acknowledge a degree of expertise in your field."
Alternatives: "recognize a level" or "admit a certain extent".
He never ceased to acknowledge a degree of genius in Shakespeare, yet spoke of him as "a drunken savage".
But as greenhouse gas emissions are a global problem, rich nations acknowledge a degree of self-interest in helping developing countries to invest in clean technology.
With some questions we acknowledge a degree of subjectivity in interpretation of their meaning, but there was a trade-off between attaining as large a sample as possible and keeping the questionnaire to a manageable size.
Though de Waal stopped short of placing bonobos in a state of blissful serenity (he acknowledged a degree of bonobo aggression), he certainly left a reader thinking that these animals knew how to live.
On a front row that included Diane Von Furstenberg and Valentino, the gossip centred on one question: would Galliano accompany De la Renta on his final bow, acknowledging a degree of authorship of the collection, or would the internship turn out to be a mere footnote in the De la Renta story?
Though breaking into the top 150 for the first time would be a big step, Kuznetsov, who was a highly touted junior before the accident, acknowledged a degree of frustration with his overall progress in the six years since his injury.
Acknowledging a degree of loss of generality, we have limited the number of femtocells to two primarily for two reasons.
Theories abound about who might have committed the murder some suggest it was Pius's father, or possibly a local drug dealer and it's difficult to talk about the case without acknowledging a degree of doubt about the true identity of the killers.
Nearly 11% did not disclose a degree preference before ASSIP but acknowledged a degree of interest upon survey completion.
At this stage, as is traditional, I have to acknowledge a certain degree of chaos, confusion, and excitement.
Given the current poor economic climate, these results are conservative and we acknowledge a higher degree of variance.
