The Tangerines were seconds away from knocking out Fulham at Bloomfield Road when Kieran Richardson lashed the ball home to cancel out Nathan Delfouneso's strike deep into injury time.
The Championship outfit had their chances in extra time only to see Brede Hangeland's header break Blackpool hearts in the 116th minute and hand Fulham the chance to travel to either Manchester United or West Ham in the next round.
"It was not a nice way to lose, and when it is the last kick of the game it is hard to get them going again," Thompson admitted.
"But it was a great strike. Two of our centre-halves went for the same ball and the ref says as soon as they head it he'd blow the whistle. That was the disappointing thing about it."
Hangeland's winner came from a Damien Duff corner, and Thompson was disappointed to have conceded from a set play at such a crucial time.
"You've got to defend your set plays. They put quality in there and if you don't defend them you are going to be punished. But I thought we played some fantastic football on a very tricky surface."
Thompson also reiterated his desire to be appointed as Michael Appleton's permanent successor by Blackpool chairman Karl Oyston, adding: "It is something I want to be - I am ready to be a number one.
"But it is Karl's decision. Whatever he does I will support it, whatever role I have at this club."