Mohamed Salah scored Liverpool's only goal early in the second half.
"We know, when we play Liverpool, it's going to be tough, because they can build and pass, and be direct as well," Maddison said after the game.
"It's a case of staying in the game. We're a top team now, we've got quality, and if we get chances we can put them away. It showed, because in 10 minutes we turned the game on its head.
"Alisson is obviously having a bit of a tough time at the moment, but I'm sure he'll be back. I'm just glad we could take advantage of his mistake."
The best chances of the first half fell to Vardy and Roberto Firmino, with both teams lucky that their goalkeepers were on top form to leave it 0-0 heading into the break.
Trent Alexander-Arnold was denied by the crossbar before the hour mark before Salah broke the deadlock on 67 minutes.
Alexander-Arnold's shot was blocked by the Leicester defence but only ricocheted as far as Firmino who, without looking to see if he was there, tapped the ball back to Salah. He then calmly slotted the ball past Kasper Schmeichel.
Leicester had a double VAR review on 77 minutes which saw them lose a penalty but score the resulting free-kick.
Harvey Barnes was brought down by Thiago on the edge of the box and referee Anthony Taylor awarded a penalty, which was overturned to a free kick following a VAR review, and Maddison curled it into the corner of Alisson's goal.
There was a VAR review for offside but the goal stood.
Moments later Vardy scored Leicester's second after Alisson stormed out of his goal and missed the ball, leaving an empty net for the Leicester striker to score in.
Barnes completed Leicester's win with a creative run down the left and into the box where he guided the ball past Alisson.
Liverpool boss Jurgen Klopp told BBC Sport afterwards: "It was a clear game that we should win. We played good football, dominated possession, took the game out of Leicester but apart from that we were really top in the game.
"We scored a goal, could have and should have scored more, whatever. Everything fine and then penalty, free-kick, offside, not offside, goal. That had a proper impact. That is something that has to change. The first goal for me is offside. The difference is we think it's an objective thing but it's not."