Shoot at short range, maybe 15 or 25 yards. Once you get it adjusted to shoot to point of aim at a short distance, you are ready to try at 50 or 100 yards.
Where did it shoot, and at what range? Were the bullet holes close together?
The more information you can give, the better answers you will get.
On a peep sight, the bullseye should be half-covered by the top of the front sight, or be just above it. You eye should automatically center the top of the front sight in the peep aperture. Concentrate on the front sight and the target, do not try to focus the peep hole.
Here is a good forum discussion about how to use a peep sight: How to Use Peep sights