A few years back our dog put his teeth through my mum's asthma inhaler and got all the gas/air in his mouth.
His eyes were almost rolling in his head, but after a few hours he perked up and lived for years. My mother didn't tell anyone what had happened until after the recovery.
If the vet is unconcerned please don't worry. Dogs and cats eat some crazy things - some are very poisonous, but it sounds like adidas isn't harmful to canines.
We all feel a little guilty is somethig like this happens - it is all part of being a responsible owner.