Ex-Denmark international Molby believes that the club will now "swallow their pride" and allow Suarez to take his punishment on the chin.
"It is unprecedented that Liverpool should be punished for something one of their players did while he was on international duty. They have no right of appeal and hopefully the reason behind that will be explained in FIFA's report," he told Eurosport.
"For their part, Liverpool have learnt from mistakes in the past. They will take their time and get the advice that they need and see how is best to take this forward – if indeed they wish to do anything.
"It may be a case where Liverpool swallow their pride and allow Suarez to take his punishment and move on."
Molby went on to criticise the Uruguay national team for defending Suarez, insisting that the forward should be held accountable for his actions.
"The environment in the Uruguayan camp is far from helpful either. It is becoming a problem that he is currently away from Liverpool as he will be taking advice from people who will be trying to convince him that he is innocent and has done nothing wrong," he added.
"The other times when he has been in trouble he has been in Liverpool which has given the club the opportunity to sit down and talk with him. The big issue here is that these people are going to try to brainwash him into him believing that yet again he is the victim.
"Uruguay are trying to defend him, even when it is indefensible. It has reached the stage now where there is no rhyme or reason for this."
Rumours linking Suarez with Real Madrid and Barcelona intensified in the wake of the incident.