The asp, the basilisk, the lion and serpents in general are considered attributes of Satan. Other demonic animals are cats (especially black), black horses and dogs, several breeds of dogs, squids, spiders, goats, bulls, bats, wolves, toads and flies. Scorpions, cockroaches, rats, shrimps, crabs and lobsters are sometimes considered diabolical too.
There is an explanation for some of these animals, but not for all. Serpents are associated with Satan because of Eve's temptation, black animals mainly because of their colour (see Demons and colours), bats for they are nocturnal (and maybe for their association with vampires), being the night associated with the power of darkness, bulls due to the depiction of some ancient gods that Christian theology turned into demons (some of these gods were depicted in human form with the head of a bull or wearing bull horns) like Moloch, Baal, the shedu, etc., and felines presumably because of their eyes, according to some folkloric superstitions (they are mainly nocturnal, and besides people feared the shining of their eyes during the night).
Goats were said to be preferred for the Devil, because it was believed that he took the shape of a male goat to be present in the Sabbaths, and many priests and judges of the Inquisition believed that zoophilia was practised during the Sabbath with this animal. De Lancre was a firm supporter of this idea. Some authors preferred to describe a figure more similar to a satyr, part goat, part man. As the demon Azazel was associated with a goat, it could have had an influence on this belief.
The toad was believed to be used as a parody of the Christian host, being, according to what interrogators investigated during the witch trials (supported by the belief of many ecclesiastic scholars), cut and distributed among the attendants to the Sabbath during the Black Mass. Besides, there is an allusion to toads or frogs in the Book of Revelation 16:13-14
Flies were associated to Beelzebub due to the meaning of the name: Lord of the Flies.
Several of the plagues that suffered Europe during the Middle Age and Renaissance were due to the immolation of hundreds and hundreds of "diabolical" cats, and the subsequent proliferation of rats. France was the country that more cats killed, most of them thrown alive into fire.
To have a black pet (or another "diabolical" animal as a pet) could be enough during the European Middle Age and Renaissance for an accusation of practising witchcraft or having made a diabolical pact.