The Hoops boss signed a one-year rolling extension on his contract earlier this week but knows it could be his last at Celtic Park if he fails to halt Old Firm rivals Rangers who have taken the last three premierships.
"Three years without the title is a long time for us. It is imperative that we do win it,” he said.
"From my own point of view, if you go two years as an Old Firm manager without a title, it might be very difficult to keep your job. It will depend on what the season brings.
"We want to make inroads in Europe this season as well.
"We feel we have good natural talent and a good young team, and with a bit more experience in there we feel we can have a go at that as well. I don't think there will be more pressure.
"The pressure of the job is always the same: win the league.
"I have had one go at it. The fans might get a bit fed-up if we miss out on a second one.”