Managing director Derek Llambias has outlined the club's desire to present "a fair and even-handed disciplinary process" to prevent future incidents going unpunished
The youngster collided with the Frenchman during Sunday's 2-1 win for the Latics in a horror over-the-ball tackle, with Magpies manager Alan Pardew claiming knee ligament damage after the game.
"We are disappointed to learn that the FA is not going to charge the Wigan player. 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," said Newcastle's managing director Derek Llambias said in a statement.
"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.
"Whilst we understand that the current procedures give the FA limited options, it cannot be correct that the most serious offences - those which have the potential to cause another player serious harm - can go unpunished, even if the original incident was seen by match officials.
"We will now be making a strong representation to the FA and the Premier League to see how a more appropriate, fair and even-handed disciplinary process can be introduced at the earliest opportunity to prevent incidents of this nature going unpunished in the future."
Whelan insisted on Monday that Manaman "got the ball, as clean as a whistle", despite Latics boss Roberto Martinez admitting after the game that it was a poor challenge before defending McManaman's character, and Llambias has questioned the chairman's motives.
"I am therefore disappointed and surprised by the comments [Whelan] made yesterday, in particular his assertion that the tackle by Callum McManaman "was a fair challenge".
"It is our strongly held opinion that the tackle on Massadio was extremely dangerous and is the type of challenge that has the potential to cause serious harm and such was the force, and reckless and dangerous nature of the challenge, even end a player's career.
"It was not a fair challenge. This view is shared by countless former players, referees and well-respected media commentators. Indeed it appears to be only Dave Whelan who takes a contrary view."