Most times the buyer is not there for an appraisal. Your agent can try to give three comparables. However, I was recently chastised by an appraiser because he said he's not allowed to take any comparables or to use comparables given by the agent. He just wanted a copy of the contract.
If the house appraises for less and the owner wants to sell, then the lawyer can show that the home appraised for less and get the price lowered to that amount, which is good for you. We just did this a couple of weeks ago. The mortgage company said in this market they wouldn't allow the buyer to put down cash to cover the gap. As your agent, I would recommend against this, too.
Another option is to challenge the initial appraisal if it doesn't appear sound or to see if you can get another appraisal. If you get another one, sometimes the seller will pay for it or split the costs.
Don't be afraid. Know that appraisals can be a pain, but are trying to cover the bank's butt and yours. Question the appraisal details. If it appears sound and the price didn't meet yours, you should ask yourself "why am I trying to pay this much anyway".