David Lopez was bundled over by David Goodwillie five minutes into injury-time and picked himself up to score from the penalty spot to send the Seagulls home with a point.
But Appleton revealed that fourth official Peter Wright was urging referee Robert Madley to blow for full-time moments before the decisive incident took place.
He said: "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 it's cost us.
"We did look comfortable. We controlled the game in terms of we knew exactly how Brighton play - there was a gameplan in terms of how we would set up and how we would deal with it.
"Their keeper was certainly a lot busier than our goalkeeper on the night.
"I think if we'd have got the second goal we'd have won the game comfortably."