With the Celtic Champions League in the future somewhat less than true after the 1-1 draw with AEK Athens earlier in the week, Rodgers left out key players in Tynecastle.
But the performance was far from inspiring and, after a disagreement with the board over the club's transfer business during the summer, the future of Northern Irish at the club has been questioned by fans.
But the manager, who won the local hat-trick with Celtic last season, insists he is happy with Parkhead.
"I love my life here," Rodgers told BBC Radio Scotland.
"I have three years left on my contract and I love every day of my life at Celtic."
"Despite all the reports, we talk about ultimatums with the council, I do not work that way, my communication is very open, so that's certainly not the case.
"And I read somewhere else about leaving.
"I have three years left on my contract and I love every day of my life at Celtic.
"All I want is for us to improve all aspects of the club.
"I can not talk about the players we want in.
"Of course we want quality players, but there are still improvements in this team, this team, many young players, so we will continue working and improving.
"It's a disappointing result for us." We had a good performance in the middle of the week and we drew, but you move quickly to football. "
After beating Hamilton 4-1 on the opening day of the season, the Hearts have now achieved maximum points in the league.
And the Jambos beat Celtic 4-0 last season, inflicting their first defeat of the season.
Since Rodgers took over the club, no team has been his team more times.
Celtic go to Greece next week in a decisive match in the Champions League.
The Scottish team will have to score at least once to advance to the group stage after AEK scored the visiting goal in Glasgow last week.
If the proper competition is not reached, the season will get much worse just a couple of weeks after it has started.