Lennon, who has just served a two-match touchline ban for criticising Scottish Communities League Cup final referee Willie Collum, has been issued with a notice of complaint accusing him of breaching three SFA rules relating to Hearts' 2-1 victory at Hampden.
Lennon ran on to the pitch to confront Norris over the handball decision that led to Craig Beattie's penalty winner, which came just before Celtic were denied a similar claim.
The Celtic boss, speaking for the first time about the incident with Norris, said: "I deeply regret what happened.
"I will be sending correspondence to the referee as an apology as well. It's one actionable thing that I've done that I shouldn't have done.
"I will go to the tribunal and hopefully get a fair hearing as I did the last time and take what's coming."
The two other charges Lennon face relate to comments made on Twitter.
The Hoops boss tweeted soon after the game: 'Referee told players he thought Wanyama handled...feel so sorry for players and fans..I think it's personal myself.' He then re-tweeted a comment from a Celtic supporter which suggested the club "pack our bags and get out of this league that is run by crooked SFA officials".
Lennon added: "It was an instinctive reaction action born out of frustration more than anything else.
"I know I have to conduct myself better than that. I don't want to talk about that (tweeting) now, I will discuss my case on Thursday."
Source: PA
Source: PA