Rodgers left Celtic last month for Leicester City last month, sparking an angry reaction from supporters of the Scottish Premiership champion, with some fans mocking its former manager with banners and chanting.
The former Liverpool boss won seven major trophies in Scotland and was on course for a third consecutive domestic treble with his boyhood club when he departed for the Premier League.
The latest flash point in the saga came this week when Rodgers' house in the region, where his wife and stepdaughter still live, was broken into in a burglary.
Discussing reports that his medals were among the items stolen, Rodgers told reporters: "Yep, so I'll have to try to get some more!"
But while assuring that his family were both safe, Rodgers was adamant that the break-in would not tarnish his memories of a successful time in Glasgow.
"It's obviously something that's not nice for any family to go through, of course," he said. "It gave the girls a fright.
"However, the only thing I want to say on it is that probably, in the last 10 days, there's been a lot around my move to here and obviously the events of the last couple of days.
"I don't want to detract from [the fact] we had an amazing time as a family in Scotland - in Glasgow, in particular.
"The people there were amazing, the experiences that we had on and off the field will live with us, and we're not going to let something like this, or some of the reaction over the last 10 days, cloud any of that.
"We dealt with it. There's been a great support out there for us and they're both fine, which is important."