Women who have not had children or those who have had cervical surgery may have a cervix that is smaller in diameter than the IUD applicator.
If you strongly wish to try again, the cervix can be dilated.
One trick is to use a medication used to soften the cervix for induction of labor: Cervidil. This is off label (not an approved use in the package insert) and there is not a lot of scientific evidence to support its use. The medication can also have side effects and will increase the cost of your procedure. However, theoretically it could help.
Even without Cervidil, the cervix can be dilated after it is numbed with a local anesthetic.
Your doctor may have a set of these, Os Finder cervical dilators:
http://www.medicalresources.com/images/PRE1030585.jpg
These are soft, malleable dilators that can help find the direction of the canal in the cervix and gently stretch it.
Insertion of an IUD is a skill that improves with a lot of practice. If you have already had a failed insertion attempt, I would suggest finding someone who does a lot of them. Also, a difficult insertion can increase the risk of perforation of the device though the muscle of the uterus. Ask for the positioning of the device to be checked with ultrasound at the time of insertion.