Your agent should be able to answer this question for you as long as you have your own agent and are not working directly with the agent of the seller (you need to be represented in agency capacity, not in a custoemr or dual agency scenario).
If you are financing the property and the appraisal came in below the contract price, our standard Realtor sales contracts have contingencies for appraisal. If the box was checked that it is subject to appraisal, and the appraisal came in below the contract price, then you are not obligated to complete the purchase but the seller is not obligated to reduce price either.
If you were expecting a higher appraisal for equity purposes but the appraisal still came in high enough to support the purchase agreement, then you are still obligated to complete the purchase or forfeit your earnest money.
All that being said, if you are happy with the property and the price, and the appraisal was high enough to support financing - why wouldn't you consummate the transaction? It is, after all, the same property and price. As long as there were no material changes or defects. If something else is bothering you, talk it over with your agent.