Lennon received a six-match ban in total, but half of the punishment is suspended until the end of next season.
An SFA ruling read: "The judicial panel found Mr Lennon in breach, but imposed no further sanction based on the fact he was not responsible for the posting of the actual tweet."
Lennon was found guilty of misconduct by the panel after running 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 tweets in question, which sparked two charges, appeared on Lennon's @OfficialNeil account on the social networking site.
The first read: "Referee told players he thought Wanyama handled...feel so sorry for players and fans...I think it's personal myself."
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" was then re-tweeted on the account. However, it appears the SFA could not prove that Lennon posted the comments himself.
Lennon this week admitted he had been out of order in his Hampden reaction. The Celtic manager 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."
Lennon added: "It was an instinctive reaction action born out of frustration more than anything else."
Meanwhile, Lennon took his place in the stands last night as Celtic earned a hard-fought 1-0 victory over St Johnstone at Parkhead. The league champions restored their 21-point lead over second-placed Rangers courtesy of a 28th minute tap-in from Republic of Ireland striker Anthony Stokes.