Lennon handed touchline suspension
Lennon ran on to the pitch to remonstrate with referee Euan Norris after last month's 2-1 loss, which ended Celtic's hopes of winning the cup as well as the league title.
Lennon was upset by Craig Beattie's injury-time penalty.
"The Judicial Panel found Mr Lennon in breach and imposed a six-match suspension; three matches to be served with immediate effect and three matches suspended until the end of next season," the Scottish Football Association said in a statement.
The outspoken Lennon, who has said he will apologise to Norris, has just served a two-match ban for another instance of criticising a referee.