Least said, soonest mended.
Though this is not always true, I think in your case, this is good advice. Attempting to approach your manager at this point will simply aggravate matters, since it will show that you feel almost as though you did something wrong by not giving them a heads up, even though you couldn't help it.
Since you did nothing wrong, you're better off just to act in exactly that way and not try playing with fire.
If you do say something about it to your manager (for instance, if they ask), make it totally casual. Something along the lines of,
Oh, yes, I meant to let you know I was applying for a transfer, but it went a lot faster than I expected, so I didn't have time.