With the score at 1-0 and Motherwell testing Celtic goalkeeper Craig Gordon on more than one occasion, former Manchester City and Swansea City winger Sinclair went down in the Well penalty area under the challenge of Cedric Kipre.
Replays showed 20-year-old Kipre making contact with Sinclair as the attacker sped past, but the contact is little more than minimal as Sinclair throws himself to the floor. Thomson sided with Sinclair, sending Kipre off, and Moussa Dembele scored the penalty.
It saw Celtic kill the game off with Motherwell having almost no chance of coming back from two goals down to beat Rodgers side, who have now gone unbeaten in domestic football for 65 matches.
But with the score at 1-0 and with 11 men still on the pitch, Motherwell could still have equalised and former Hearts midfielder believes just that - calling Thomson's decision 'horrendous'.
So disappointing, not just for Motherwell but any neutral, to see the referee make such a horrendous huge decision in a Cup Final— Michael Stewart (@mstewart_23) November 26, 2017
Celtic had taken the lead early in the first half through Scotland international James Forrest, after neat play from Callum McGregor gave Forrest a yard of space to curl a left-footed effort past goalkeeper Trevor Carson.
The Hoops have now won four trophies since Rodgers took over, completing a treble last season and they look likely to do exactly the same as they remain at the top of the Scottish Premiership and drawing Brechin City in the Scottish Cup.
Rodgers takes to the dugout once again on Wednesday night as they return to league action, as they travel to Fir Park to face Sunday's opponents as Stephen Robinson's side look to exact revenge.