Yes, it is OK to have gas receipts and not mileage. At this point you would have to deduct actual car expenses (gas, repairs, maintenanance, depreciation) and you would not be able to take standard mile rate deduction.
However, if you want to take a standard mileage log, you do need to know how many miles you drove for business purposes. You can recreate the log - get a calendar and estimate (as closely as possible) how many business miles you drove each day... it's a lot of work but can be done.