Bowyer, 41, the sixth man to take charge of the side in the last eight months, was handed a 12-month contract after keeping Rovers in the Championship with three wins and a draw at the end of the season.
But he told BBC Radio Lancashire: "They've not said 'regardless of what happens you are here all season'.
"I've grown up in the industry all my life so I know what it's about. If we were to lose three games on the trot then there would be pressure."
The former youth-team boss added: "I'm under no illusions. The only person that can give me assurances is me and the players and that's by the performances and the results."
Bowyer brought in Terry McPhillips as his assistant and Tony Grant as first-team coach this week and is not expecting to sell leading goalscorer Jordan Rhodes.
"From conversations with the owners they categorically told me that Jordan Rhodes wasn't for sale, and I'm led to believe that," he said.