The pagan gods (Egyptian gods as well) were known for their capriciousness and volatility. They were petty and unreasonable and could lash out or punish their human subjects for no apparent reason (like demons and monsters, and much like ancient dictators and rulers); especially if the expected sacrifices were not delivered on time. That is why they were so feared by the pagans who constantly had to appease them with sacrifice (sometimes even human) and ritual, so that their gods' wrath does not flare up and bring upon them disaster. This has a lot to do with how they identified their gods with nature, and the logic goes like this: Since nature is capricious and strikes at civilians for no apparent reason, then it must be that the divine is capricious as well (nature they believed is an embodiment of the divine), thus the only way to keep them at bay, they believed, is through sacrifice, gifts and appeasement. Greek mythology is replete with such imagery in which a god gets angry with a human being for some petty offense, whereby a sacrifice is quickly offered to appease its wrath.
Moses here was using the Egyptian/pagan belief system to his own advantage. He was telling Pharaoh, we have a festival now, our God is expecting sacrifices from us, if we do not deliver them on time he might punish us and send pestilence or some other horrible death, that is why you must let us go. Pharaoh could very well relate to this, and Moses thought it would appeal to him and he would let them go, but, alas, Pharaoh would not hear of it.