The club said that it is "surprised" and "disappointed" by the Scottish FA's decision, questioning the validity of its disciplinary policy.
"Clearly we are extremely surprised and disappointed by [Wednesday]'s decision," read the statement.
"Fundamentally the particular disciplinary system in place is absurd - a system where such a case can be brought on the strength of two 'complaints' from people totally unconnected to the match in question, while a fourth official overseeing the technical area during the match makes no mention of any incident to the SFA.
"Despite even supportive comments from numerous individuals including Jim Goodwin himself, this judgement has been made, something which we find quite astonishing.
"It is clear that this decision will have huge repercussions for the game in Scotland and we are sure Hampden Stadium will be a very busy place now every Monday morning."
Lennon will miss Celtic's potentially title-deciding clash with Inverness Caledonian Thistle this Sunday.