The game eventually ended 1-1 after seven minutes of stoppage time played. Rovers, who had been in the lead since the 45th minute when Jordan Rhodes netted from the penalty spot, saw the full three points slip away when David Goodwillie brought down David Lopez in the box and the victim scored from the spot.
But Appleton had concerns about why the penalty was given in the first place as the game should have been over long before it was awarded.
He told reporters: "The most disappointing thing - I've got to be careful what I say a little bit - is for 45 seconds the fourth official is screaming down his mic to the referee 'that it's, it's done, it's finished'.
"So to concede after that is disappointing. Having said that, it was a silly challenge from David - he knows that - and its cost us."