You have not really given us enough information to answer your questions specifically.
However, in most cases, you are without solid options.
Let me explain...
Generally, an offer gives the opposite party (the seller, in this case) a time period by which they must respond. It can be 1 hour or 100 years - it is up to the offeror (the buyer, in this case). Common is somewhere between 'by midnight on the offer date' to ' within 5 business days'. If you had a similar clause in your offer, and they accepted the offer AFTER that time / date - you have a real solid case. Essentially, they accepted an offer which was no longer valid; thus, there is no contract.
If, on the other hand, they accepted your offer within the prescribed period of time, you now have a contract. Your only recourse is to review the default provisions of your new contract. Expectation would be very low to assume you can default on the contract and then come back with a lower offer that they would accept.
Welcome to the School of Hard Knocks. I have learned so very much here.