Llambias was incensed after the Football Association (FA) said it would not be taking retrospective action against Wigan Athletic's Callum McManaman following his knee-high tackle on Newcastle's Massadio Haidara on Sunday.
France Under-21 international Haidara had to be carried off on a stretcher during the first half of Newcastle's 2-1 Premier League defeat and is now set for a spell on the sidelines.
The FA said on Tuesday it would not be taking any action against McManaman on the principle of avoiding the "re-refereeing of incidents" that had been seen by at least one of the officials.
"We are disappointed to learn that the FA is not going to charge the Wigan player," Llambias said in a statement on the club website.
"We were first notified of this decision by a national media outlet who received notification from the FA confirming the decision. This was prior to anyone from the FA having the courtesy to contact the club to let us know.
"It is clear from this decision that the current disciplinary procedures are not fit for purpose. Newcastle United, along with other clubs, have had players suspended for incidents reviewed after the game. Whilst not trivialising these incidents, they were not, in our opinion, of the seriousness of Callum McManaman's tackle on Haidara."
"I have the greatest respect for Dave, who has been in the game for a long time as a professional footballer and now owner. I am also aware that Dave's career was cut short due to injury," Llambias added.
"I am therefore disappointed and surprised by the comments he made yesterday, in particular his assertion that the tackle by Callum McManaman "was a fair challenge"."
