Mahrez was blocked from joining Manchester City and then went AWOL for almost two weeks.
Vardy told Sky Sports: "The bid came in, it was turned down, and you can understand his disappointment. But while he wasn't here we were having to get on with it.
"We are all professionals and had to play without him. It happens if he is injured or on the bench, so we just focused on the games. He came back, got us in the dressing room, explained the situation, and you move on.
"Everyone is exactly the same, they know what they have to do and their jobs. It was Riyad who wanted the meeting and got everyone in the dressing room and explained the situation, which is kept behind closed doors between us, and as far as everyone else is concerned that's that.
"You have to make sure it's like that, with the dressing room we have got everyone is a close-knit group so for him personally to want to do that shows what he is about."