The Foxes are experiencing a down season after winning the FA Cup last term and narrowly missing out on Champions League qualification.
Rodgers' side face Danish club Randers on Thursday in the play-off round of the Europa Conference League.
"The nature of football is that there isn't so much time," said Rodgers.
"It wasn't so long ago that you are deemed an elite manager, having won the FA Cup but then very quickly you're not.
"But I get that. That's the game. What's important to me in life is to do your very best. I feel I'm doing that here with what we have and together we have made some great steps.
"I love the people at the club, I love working with the players here and that's all I will continue to do. I will do that with a smile until someone tells me differently.
"And if they do, I will have done my very best with the resources that I have and then I'll move on. But until then I have a big energy for the team, for the club and for my contract."