The truth of a statement has come to us via (by way of) the "accused" person. He has said in his own words that he did it. He has admitted it.
The manager has said that he made a big mistake in/by taking a week's vacation at a very bad time. He admits he should have remained on the job during the audit, to help out during this very critical time, and to be available to answer important questions from the auditors, which other employees might not have the answers to , etc.