Celtic boss 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 said: "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.
"I saw the greatest manager in the game last night (Sir Alex Ferguson) having a spat with Roberto Mancini and people enjoyed it, enjoyed seeing Sir Alex show that passion, that he was up for the fight.
"At times we do get lost in the game but if you take that away from us, you are going to have robots on the touchline, sitting with their hands in their pockets not doing anything.
"You can't take away the human element from managers, we are human beings at the end of the day.
"There are times we get angry and aggrieved and make mistakes in that aspect of the game but I think I get a rough ride.
"Over the course of the season, up until the League Cup final, there was not one thing I did wrong.
"We had the incident at Ibrox (no further action was taken against Lennon after he was sent to the stand at half-time by referee Calum Murray) which I have had the hearing for.
"So over the course of the season we are talking about one incident so I don't think I have to change that much but I will temper those actions if I can."
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.