Criticism has been levelled at Fenway Sports Group following the failure to bring in a replacement after striker Andy Carroll was loaned to West Ham.
Rodgers admitted he would not have let the England international leave had he not been confident he could bring in a replacement but a deal for Fulham's Clint Dempsey fell through because FSG would not pay what they considered an inflated price.
That led to suggestions the manager had been undermined by the owners but he stressed he understood the situation when he took over in June.
"I've had long conversations with the owners," he said. "I've got to say they have been very honest and very up front right from the off.
"I came here first and foremost because of the owners. I felt a genuine honesty in their approach to it and in how they wanted to go forward with the football club."