It would be better to include a concession towards avoiding similar problems in the future ("I shouldn't have ...", "I'll ... next time" ), but I don't know which such statements you can honestly make.

Also consider "I will work on figuring out how to avoid that mistake in the future", if you're not sure what you actually did wrong. Figuring out where the mistake was in the first place is an early step in figuring out how to avoid it in the future, so this covers that, without highlighting just how close to the beginning of the process you are (which tends to make people uncomfortable). It also implies but doesn't state that you will actually take steps to avoid the mistake in the future, so if you decide that the effort of avoiding that mistake is not worth the inconvenience to others, you won't have lied.