Police were called to the property near Glasgow in the early hours of Wednesday.
His wife and stepdaughter, Charlotte and Lola, were in the house and a number of items were stolen but nobody was injured.
Rodgers, 46, left Parkhead last week to take over at former Premier League champoins Leicester, sparking anger among some Celtic fans.
“For the girls to have someone come into the room, it’s horrendous really,” Rodgers said at his pre-match press conference.
“I just made sure they are secure up there. We are looking to buy a house here in Leicester and they will move down very soon.
“When I got the call in the early hours of the morning you’re worried about their safety. The reaction from lots of people has been great. We’ve been given great support.
“It’s not nice for any family to go through. It gave the girls a fright. The last 10 days there’s been a lot around my move to here but I don’t want it to detract from an amazing time we had as a family in Scotland.”
Police in Scotland confirmed an investigation was under way, with Rodgers losing several of his medals.
“Yeah, I’ll have to try to get some more,” he said.
Rodgers is preparing for his first home game in charge against struggling Fulham on Saturday.
He suffered a last-minute defeat in Sunday’s 2-1 loss at Watford in his first game at the helm.
Rodgers added: “All games are very difficult to forecast. People will look at chunks of five games and think ‘right, you can get points here’ but you never know what the other team is going to bring to the game.
“Scott (Parker) has come in and Fulham had a good performance last week, so he will want to continue with that this weekend.”
Download our app and read this and other great stories on the move. Available for Android and iOS.