The Foxes’ injury-hit squad have struggled this season and criticism of Rodgers and his players increased after Sunday’s disappointing FA Cup exit at the hands of East Midlands rivals Nottingham Forest.
When asked if he still had the board’s full backing, Rodgers said: “I’ve never felt I haven’t, but I also understand football.
“I’ve got a great relationship here with the people at the club, a very close working relationship with everyone, but I understand you have to get results.
“Whatever happens to me in the future, those relationships don’t change, they’re great people here, have always supported me.
“This year has been a challenge after challenge and primarily because of the players we have missing, but of course the weekend’s result wasn’t great, so you can’t mask over that and I would never try to.”
Leicester will bid to bounce back from Sunday’s 4-1 defeat at Championship side Forest against Rodgers’ former club Liverpool at Anfield on Thursday.
Rodgers, who will mark three years in charge of the Foxes later this month, admitted the manner of his side’s cup defeat had turned up the heat on him.
He added: “Certainly when you lose you’re always open to criticism, so I’m pretty sure that would have been the case on the Monday and that’s part of the job.
“For me, you’ll always be under pressure when you’re not getting results, you can’t deny that.
“We’ve had a great run here for a period of time, but when results (are not good), especially like the one at the weekend, that will always put you under pressure as a manager. I get that and understand that. It’s not something I shy away from.”
You’ll always be under pressure when you’re not getting results, you can’t deny that
Leicester, who have been serious top-four contenders for the last two seasons, have won only one of their last five Premier League games as an injury crisis at the King Power Stadium takes its toll.
The likes of Wesley Fofana, Jamie Vardy, Jonny Evans and Timothy Castagne remain sidelined for the trip to Anfield.
Rodgers said before Sunday’s loss that “big changes” were needed in the summer to “freshen up” his squad and he added that, although this week had been time for “reflection”, there was still plenty to play for this season.
The Foxes’ last league win was against Liverpool in December and Rodgers said: “We want to finish as high as we possibly can in the league, we’re still in a cup competition (Europa Conference League), so we want to go as far as we can in that.
“I hope that we can get players back and show our true level at some point before the end of the season, and not just the true level, but the consistency of that. That would be the aim.”