Of course and I don't think Parker did enough today to even warrant consideration to be retained in any manner by the next HC...let alone to be HC. Had the team come out and laid the wood on Nebraska without them coughing the ball up multiple times, I would say Parker may have something Purdue needs. But unless he can put a string of victories together and in impressive fashion, the entire staff needs to be let go.
My personal opinion: Parker would have to go 4-1 with impressive wins over each opponent to warrant even turning in a resume. If not, I think the next coach should seriously look at retaining him as possibly a WR and passing game coordinator to help transition the class from staff to staff. You can always let him go and find another WR coach in year 2.