Just 24 hours after his surprise sacking at Southampton, Adkins has become one of the front-runners to succeed Michael Appleton at Bloomfield Road.
Goals from Tommy Smith and Kim Bo-kyung ensured Thompson's short reign suffered its third consecutive defeat, however, while remaining tight-lipped about Adkins he was unafraid to talk of his own ambitions.
"There's always going to be speculation," said Thompson, whose side's goal came from a Gary Taylor-Fletcher header.
"I'm in charge - temporary charge - for the moment and until I hear anything different I'll keep going along but I think it needs sorting, especially for the lads because they need stability around the club.
"The players hear all the speculation, it needs sorting out. There are lads out of contract, there's lads who need the contract sorting. I'd be lying if I said it wouldn't be unsettling for them. Until we hear different we've just got to make sure we get them right.
"I've said from day one that Karl Oyston will make the decision and hopefully the right decision for Blackpool Football Club.
"I want to be number one of course I do. I've always said I'm ready, I'm ready to be number one but whatever Karl decides to do I'll back him 100%, with whatever role I have at Blackpool.
"I've just been in temporary charge. We've not actually sat down and spoken. That's Karl's decision - that's why he's chairman."
- Sports & Recreation