Krige, speaking in his column in the South African Afrikaans paper Sondag, lambasted SA Rugby for the choice of de Villiers over Super 14-winning coach Heyneke Meyer.
The former Stormers, Northampton and Springbok flanker was surprised when he heard the choice of De Villiers over Meyer.
"I was in a meeting Wednesday and I saw a message on my phone from a good friend telling me about the appointment," Krige wrote. "I didn't know if I should laugh or cry.
"For me there was only one logical choice to succeed Jake White as Springbok coach and that was Heyneke Meyer.
"Let me put it this way: Coach A and coach B are up for a position. Coach A has won internationally at Under-21 level, but has no Currie Cup or Super 14 experience. He currently is helping out at Stellenbosch University.
"Coach B has three Currie Cup titles and a Super 14 title. Above this, 70% of the players in the country want him as coach. If you need to make a rugby decision, then it is logical that coach B is the answer.
"But if you need to make a political choice, then coach A is the answer.
"Coach A is Peter De Villiers and B Heyneke Meyer - this is precisely what happened this week."
Krige placed the blame at the door of SA Rugby's deputy president Mike Stofile - who is also brother of sports minister Makenkhezi Stofile and has been pushing transformation for some time.
"Now that I think about it, I don't know why I expected anything different," Krige continued. "With Mike Stofile as chairman of the committee, it was certain that nobody who would stand up to him would be appointed.
"They appointed Peter de Villiers because they knew he would dance to their tune. He will choose the players they want him to choose, and he will be politically correct.
"If they wanted politically correct, then why didn't they choose Allister Coetzee, who is also black and has been Jake White's assistant for the last four years?"