I'm not sure it was so much either, though certainly pious Romans both respected and feared the gods they belived in.
But it was done largely for expectation of gain. They thought the gods helped grow their crops, grant victory in battle, and heal diseases, etc. Paganism has a certain mercantalist aspect to it. You believe gods xyz have some kind of power over the universe, so you want to get on their good side. If you're on their good side, you supposedly gain their favor. If you're on their bad side, they ignore you - or worse, harm you.
If a sect of Romans were faithful in offerings to a certain deity, but something bad happened to them regardless of their placations, it was assumed the deity had not lived up to his side of the relationship, and the followers were free at that point to take all the cult objects of the deity in question and defile them in anger. This sometimes happened. This is probably the "blasphemy" you speak of. But blasphemy is really the wrong term ... it's more like dissastisified customers breaking a contract and smearing the business reputation of the CEO concerned.