Both men are accused of adopting "a threatening and aggressive attitude towards an opposing member of team staff" during the Scottish Premiership game which County won 2-1, while Lennon is also accused of "the repeated use of offensive, insulting and abusive language."
The pair, who were both sent to the stand during the match by referee Willie Collum, have until March 5 to respond ahead of the March 13 hearing.
The row centred on Adams' reaction to challenges made on his players by St Mirren captain Jim Goodwin.
Ahead of the home league game against Kilmarnock on Saturday, Lennon said: "Passions rise high in a game but I would like to take this opportunity to unreservedly apologise to Derek Adams and his staff and more so, my own supporters for their manager getting into a bit of controversy with the officials and being cited for that.
"I have a lot of respect for Derek Adams and what he has achieved in the game although my words and actions didn't reflect that last Saturday.
"As far as I'm concerned it is water under the bridge and we will wait to see what the hearing brings.
"What I said, I said, so I can only apologise for that and we move on."
Saints have won one game in their last 11 and find themselves in the relegation play-off spot which Lennon admits is hurting him.
And while the Paisley side are only three points behind eighth-placed Killie, he stressed that it is time for action and not words.
"Our reputation and status within the SPFL is in question," said Lennon. "People are asking if the players are good enough at this level and if I am good enough to manage at this level.
"These things hurt. Sometimes, as a man, your reputation is all that you have.
"With 11 games remaining we must use every one of them to get our reputation back to where it belongs.
"There are three points separating four teams so it shows how competitive and tight it is.
"We are doing everything within our power to turn it around and I do believe that I have the right people in that dressing room.
"But the talking has to stop, the action has to happen on the park."