I agree with Bob and Bill.
Keep in mind that you might put your deposit at risk (depending upon how your P&S is written) provided you opted to walk after the contingency period has expired if the seller refuses to accept your price adjustment, and the seller might be able to pursue damages against you too.
Also, keep in mind that adjusting the price isn't your only option for adding more value to the deal. Let's say that the property appraises for less than your offer price due to some immediate repairs discovered via the appraisal and/or inspection. It's possible that you could get the seller to extend the closing date, and make the repairs. Then you could work with your lender to order another appraisal (which now meets or exceeds your offer price).
Another option, for adding more value to the deal, is to renegotiate the terms. Again, let's say that the property appraises for less than your offer price, the suggested repairs are cosmetic (eg new paint, new carpet, and updated fixtures), and you don't plan to address those repairs immediately. You could ask the seller to sell the property with seller financing (if s/he wants to get that offer price), or you could ask the seller to buy down your interest rate for a period of time.
Additionally, keep in mind if you did win a bidding war to put that property under contract, that other buyers might be less picky and willing to pay more than your appraisal amount. In that case, a seller might tell you to "take it or leave it." So, although you can renegotiate, the seller also can opt to not negotiate (as Bob stated earlier).
Be negotiable and nimble, and don't overplay your hand.