The key here is to acknowledge where you went wrong but show that you learned from your mistake, took a positive lesson from it and moved on. If you can demonstrate that you never made the same mistake again, that will impress your prospective employer.
Be specific – describe the situation and your reaction to it, outline the lesson you learned and how you would approach a similar situation today.
For instance, let’s say that in your early career you failed to deliver an important project on time because you didn’t manage your time and prioritise properly – then you can say that you learned an important lesson from this and are now a stickler for organisation and keeping things on schedule. Or perhaps in your first project management role you failed to communicate effectively with your team, but ever since then you have ensured that weekly meetings are held where everyone has input and all issues are clarified to make sure everything is on track.