A fine brace from James Maddison and a clever finish from Jamie Vardy was more than enough for Brendan Rodgers team to secure all three points and move to third in the table.
Brighton had a couple of chances in the opening stages with Danny Welbeck missing their best opportunity when Kasper Schmeichel saved well.
But after that it was all Leicester and their attacking power and sharpness proved too much for a Brighton team who have a disappointing return of 10 points from 12 matches.
Graham Potter's team are in the thick of a developing relegation battle and their next two matches against struggling Fulham on Wednesday and then and Sheffield United will be vital.
"They play nice, neat football but there is nothing at the end of it," said Shearer. "Being a forward in that team would be such a frustrating role to play. They get into good positions but their final ball is poor.
"They don't look forward often enough. Forwards are making runs but they decide to go sideways or backwards rather than having more oomph about the team.
"They don't stretch and create as much as they as they should and they have been poor. When they have balls in the box, they had nobody on the end of them.
"Brighton had their chances in the first half. They didn't take them and their heads dropped. Leicester had their chances and took them."
"They have to try and find a way of being more a of threat. Sometimes you just have get that ball forward and get into the box.
"A lot of play has been in front of that Leicester back line. Not enough in behind and the Leicester defenders have had a really comfortable evening."
Albion head coach Potter admitted it was a tough evening at the King Power and believes the failure to take one of their early chances cost them dearly.
"Disappointing. The box is where it matters and Leicester were better than us.
"We stuck at it in the second half but clearly over the course of the 90 minutes not good enough to get something from the game.
"In the end they were a little bit too good for us and sometimes that happens.
"That is our 12th game, we are quite early on in the season so we have a lot of time but we know we are fighting to improve, fighting for points.
"We are going to keep humble and keep going."