Lennon is accused of using 'offensive, insulting and abusive' language towards Goodwin after the defender's heavy tackle on Dylan McGeouch towards the end of Sunday's 1-1 draw.
Goodwin laughed off the situation joking: 'It's a good job the microphones never picked up my reply to Neil', but the SFA have given the Irishman until April 10 to respond to the complaint made by compliance officer Vincent Lunny.
Lennon said: "I can't really talk about it at the minute but needless to say I will be defending my case as vigorously as possible.
"I don't want to say anything to prejudice the case against me. I'll speak to the club officials and lawyers and we will come up with a defence to defend myself as best I can.
"Referees are entitled to have a bad day but we are entitled to have an opinion on their performance as well.
"It would be fair to say that both managers were aggrieved with the performance of not just the referee but his officials in general.
"Vincent has a job to do and he feels he has to bring this case forward and we will deal with it when it comes around.
"We will make a case and hopefully we will get what we deem to be the right result."