I'm sure you've heard someone somewhere along the line say that making mistakes is all part of the learning process. It's definitely true, but that doesn't necessarily make it any easier to own up to them. Perhaps you can let the little ones slip by or quickly correct them without notice, but I say the bigger the mistake, the more important it is to take responsibility. Confess quickly and do it right by turning it into a learning experience for everyone. From an article on the Guardian website:

Chartered occupational psychologist Dr Peter Honey thinks the key is to try and shift the focus from blaming people to blaming processes.

Honey says that mistakes are often the fault of processes rather than people involved, and offers a three-point plan for making sure you learn from them. Firstly, there needs to be an honest assessment of the whole situation. Next, you need to tease out some lessons – could you improve any processes so that this cannot happen again? Lastly, work out how, specifically, you would implement the lessons learned, so they're not just left as good intentions, says Honey.