Chairman Karl Oyston is busy interviewing potential replacements for Michael Appleton - who left for Blackburn last month - but the Tangerines' first home league win since December 15 could boost Thompson's chances.
On-loan Aston Villa striker Nathan Delfouneso was the match-winner in stoppage time, after Thomas Ince had cancelled out James Henry's opener, but Thompson refused to get carried away.
"Until I know anything different, me and my staff will prepare the players. Karl will make the right decision for the club, I've always said that," said Thompson.
"Obviously he's interviewing people, quite a few people, you never know it might get back to me. As staff and players I can't ask for anymore than what they are giving us.
"You need to have a team atmosphere and big characters around the place. We needed that, and hopefully that can kick start our season, especially at Bloomfield Road.
"It's nice to score late on in the game at Bloomfield for a change, but we've had to come from behind again.
"Why are we conceding? It's something we've got to look at, especially the first goal every game.
"It takes a lot of character to keep coming back but it doesn't show a lot of character to concede so it's not a good stat that we want here."
- Sports & Recreation
- Michael Appleton