The former Manchester United and Preston midfielder was quizzed about the speculation after his side registered a third win in four league games with a 2-0 home success over Crewe.
Wes Thomas headed the hosts in front from Jon Harley's cross after just two minutes and when Thomas went down under pressure from Andy Bond, Izale McLeod stepped forward to convert the subsequent penalty 16 minutes later.
Asked if all the managerial talk had been a distraction, Appleton said: "I can't control what other people around me think - how the fans and players react to it. But I've got a tough enough job here to start worrying about other jobs."
Appleton said it was always going to take time for his makeshift side to hit form after signing players on loans and month-long deals to keep his cash-strapped side competitive.
He said: "I'm happy. I said when people were getting excited after a couple of games that it might take until November to see the best of this team. We've got so much work to do and the players are nowhere near at their best at the minute."