The 41-year-old stepped down as boss of League One side Oxford United in the summer to link up with Craig Shakespeare at the King Power Stadium in an assistant capacity.
Asked about the speculation linking him with the position on a full-time basis, the former Portsmouth, Blackpool, Blackburn and Oxford chief told Sky Sports News: "I've made it very clear that I came here as an assistant manager, signing a three-year deal.
"I walked away from management in League One. I'd just love the opportunity to honour the contract I've got at the minute. Beyond that, it's out of my control.
"It's obviously been a difficult week, so we are delighted with the performance today. To produce a performance the way we did after the week we've had, the players deserve a lot of credit. Getting the first goal was massive.
"That's only the second time we've done it this year, and they've both been in the two wins we've managed. That was important. I'm delighted with the way we stuck at it, too. When they pull a goal back, it would have been quite easy to have gone on to draw, maybe even lose the game."
Appleton is expected to remain in caretaker charge for Tuesday's EFL Cup home tie against Leeds United.