Neal Maupay put the hosts ahead from the penalty spot in the 35th minute, sending Kasper Schmeichel the wrong way, and Danny Welbeck doubled Brighton’s lead just after the break with a well-timed header.
Jamie Vardy pulled one back for Leicester before they had two equalisers ruled out in the final stages, with Harvey Barnes judged to be offside and obstructing the goalkeeper on both occasions.
Maddison did not make a significant impact on the game and was replaced by Ademola Lookman at the break, who played a role in his side’s opening goal.
“(You need to give Maddison) Time, patience, support. It’s understanding that no matter how confident someone is and how good a player they are, they will always have a period in their career where confidence isn’t quite there,” Rodgers insisted.
“You always have to take them back to the basics. You’ve got to work your socks off and work even harder. I always feel that if you do that, that gives you confidence. I’ve seen it so often.
“He’s a brilliant talent and has played many fantastic games for Leicester and he will do that. He’s just in a little moment where it’s not quite happening for him.”
Brighton manager Graham Potter was left delighted after a fourth win from the opening five matches left them fourth in the Premier League, just a point adrift of the leaders.
“It’s a great three points for us in front of our own supporters. I thought they were amazing today our fans, got behind us and helped us out when we needed them,” Potter said.
“I thought we played well, we played well to get the lead and had to do lots of things well – defend, attack, the bit in between, I thought we did that well.
“Obviously Leicester are a quality side, they responded well, they scored a good goal and we had to hang on, we needed a bit of luck. The margins that got away from us last year were in our favour today and we managed to hang on for a fantastic three points.
“There’s no getting away from it, it’s a great start from us, but that’s all it is. It is a start and there’s a long way to go but we’re delighted with the points tally so far.”