The Parkhead manager sidestepped questions about reports Steven Gerrard could depart Ibrox to Aston Villa and what effect it may have on the Hoops' title prospects.
Instead Postecoglou insisted everyone inside Celtic Park must focus solely on ensuring momentum is maintained in the east end of Glasgow.
When asked about the uncertainty over Gerrard's future, the Australian said: "They're the kind of distractions I avoid, to be honest. I've been really laser-focused on here, and I'll continue to be.
"I'm just making everyone really aware that we can't get distracted by anything or anyone else. We're trying to build something here, and when you're trying to build something, and be successful, you can't afford to be looking over your fence at what other people are doing.
"We've got to build our house, make it nice and beautiful and then see how it stacks up against the rest of the neighbourhood."
Celtic have won seven of their last eight games in all competitions since the start of October and Postecoglou has been named cinch Premiership manager of the month.
Postecoglou said: "It's been a good little period for us. We'd been a bit unsettled in the previous month and results and performances were up and down so we had to get some consistency and momentum. The whole group's been outstanding through this last period, both domestically and in Europe.
"The award is great but it's a reflection of how well the group is developing. It's really important people don't think this is on the back of something magical I'm doing. It's the whole group - staff and players - that's working really hard."