First of all, if you haven't done so, reset your device. It's always a good idea to do this after updating. Resetting might remove glitches you'd experience otherwise.
Here's how to do it: press and hold Home and Power button until the Apple logo appears. Let go of both. The iPhone will power up on it's own.
If this doesn't help, it's necessary that you tell us a bit more about your issue:
Which iPhone is it, and which software is installed; what do you use to store your contacts (email account, something different); are the contacts backed up (iCloud or iTunes), and whatever else you think could be important to help us understand your problem.