Williams, who is hoping to face the British & Irish Lions in this summer's three-Test Series, was suspended by a Sanzar judicial committee on Tuesday after being found guilty of stamping on Crusaders flanker Richie McCaw during their Super 12 loss on Saturday.
Williams was sent-off by referee Paddy O'Brien after the incident at a ruck.
Blues chief executive David White believes the six-week penalty was excessive and said: "We are concerned that a literal application of the laws of the game by citing commissioners and the judicial committee is not consistent with the way the game of rugby is played, and the way in which similar incidents are dealt with on the field.
"There is a serious concern that there is a lack of clarity about the distinction between rucking and stamping offences."
White also felt the decision was particularly harsh as it could affect Williams' prospects of New Zealand selection as he would be out of action until May 3.