Just started terraria last week for the first time.

Prehard mode, on expert.

wiki says 1/20 chance for face pet to spawn.

64 Brains, zip. 23 brains in one go. That took a while to collect and save enough for summons.

Got the Eater pet on the 4th try. Am I doing something wrong?

Nope. The drop chance just never gets to 100%, no matter how many simultaneous kills you score. You may get it after the first try, but you may also never get it at all. But it is more likely to get then not.