The Hoops were denied a chance to go for an Scottish Premier League and Scottish Cup double by Sunday's 2-1 loss at Hampden.
Lennon was incensed by the decision to blow for the late penalty from which Craig Beattie scored the Tynecastle side's winning goal.
At full-time he stormed on to the pitch to confront referee Norris, who had given the spot-kick after a shot from Jambos skipper Marius Zaliukas hit the arm of Celtic player Joe Ledley.
Lennon, who has three disciplinary cases pending with the Scottish Football Association, was also enraged when Norris refused them a penalty in injury time when the ball appeared to come off the arm of Hearts defender Andy Webster.
The Celtic manager avoided the post-match press conference but used his Twitter account to blast Norris.
He tweeted: "Referee told players he thought [Victor] Wanyama handled...feel so sorry for players and fans...I think it's personal myself."
Later Lennon re-tweeted a comment from Celtic supporter @DazDiCanio which suggested the club "pack our bags and get out of this league that is run by crooked #SFA officials".
Lennon, who has three disciplinary cases pending, had also been angered when Norris refused the Clydesdale Bank Premier League champions a penalty in injury time when Celtic players felt the ball came off the arm of Hearts defender Andy Webster.
Lennon was written to by SFA compliance officer Vincent Lunny demanding an explanation for his comments about referees ahead of an SPL game against St Johnstone at Celtic Park at the start of the month.
The Parkhead boss is fighting two other charges relating to criticism of referee Willie Collum after the Scottish Communities League Cup final defeat to Kilmarnock and his half-time dismissal by referee Calum Murray during the recent 3-2 SPL defeat at Ibrox.
After the defeat to Kilmarnock he accused Collum of making a "criminal decision" which "cost us the Treble".
Celtic coach Alan Thompson confirmed Lennon had also confronted Norris in the referees' room after the match.
He said: "I think he has been in, yes, but I wasn't there so I don't know what was said.
"We are all angry. We have just lost the semi-final of the cup when there were 92 minutes on the clock, it is frustrating."
Lennon continued to rage on Twitter, accusing Manchester United supporter @mccart3204 of talking "clap trap" when he suggested Celtic striker Gary Hooper had been offside for the Hoops' equaliser which cancelled out Rudi Skacel's opener.
He then dismissed as "nonsense" a comment from Celtic fan @-FlyTheFlag that the team "shouldn't be relying on decisions, the players weren't good enough".
He later added a good luck message for Hearts manager Paulo Sergio: "However I would like to wish Paulo and his team the best for the final."