Cherries boss Eddie Howe was diplomatic at the end of the 3-1 defeat when asked how he felt about a number of controversial decisions made by referee Mike Jones.
Howe said "We have been unlucky, we feel there are a couple of incidents, I believe, have gone against us."
Formerr official Hackett has now gone a step further by claiming Sanchez should have been sent off for his challenge on Bournemouth midfielder Harry Arter in the second half.
He said: "They are exactly the sort of tackles that we do not want in the game and must be dealt with firmly. I am clear that it should have been a red card."
Hackett added in an interview with the Telegraph that Jones got "three or four big decisions wrong".