We originally offered $182,500 but the owner counteroffered at $190K bc the previous contract (which fell thru)  was appraised by the bank it at $190K but we have no proof of this.

If you just listed the property and aren't desperate to sell, you can counter-offer and hope that he either negotiates higher or just stays firm (and doesn't walk). 

Would it be right after I receive a counter-offer?

Two easy ways to back out at this point:1 If they have not signed the contract that you submitted, you may withdraw, in writing, any time prior to their acceptance. 2 If they send you a counter offer, revised contract, your original offer is now void, and you simply do not sign the new contract.

@Pamela Satcher, you email back with your counter-offer. 

If the seller doesn't make a counter offer before the offer expires, there is no negotiation.I'm curious what time frame was on your offer, because if it was only  a couple days, your realtor should have gotten back to you sooner than a week!  

We initially made an offer and didn't like the counter offer, so we forgot about it.

We received an offer from a church group that wanted to lease the property, but wanted me to do about $200,000 in repairs and improvements.My counter offer to them was for them to purchase the property instead, and obtain a community improvement loan for the repairs/improvements while I would owner finance a majority of the purchase price.

The person selling the property took my offer without a counteroffer.

The seller accepted our offer and didn't counter offer.