The 20-year-old playmaker moved to Parkhead in January, swapping life in his native Australia with Central Coast Mariners for that at the top of the Scottish Premier League.
He has been eased into European football by Neil Lennon, with the Bhoys boss wary of expecting too much, too soon.
Rogic is, however, feeling settled in Glasgow and believes he is ready to fight for a regular starting berth - aiding his quest to earn a place in Australia's 2014 World Cup squad.
He told the Daily Record: "Do I need to nail down a place at Celtic to play in the World Cup? Possibly, but I'm up against a lot of good players here who can all do a job in the team.
"However, I'm improving every week at this club. I haven't had much playing time yet but that was to be expected coming into a settled squad last season.
"I just have to keep working hard, wait for my opportunity and make sure that I take it when it comes along.
"It is like a fresh start for me this season. It was a big move coming across to the other side of the world and it does take time to settle on and off the pitch.
"I'm enjoying life in Scotland now. At first it was a bit of a shock because I left the Aussie summer and walked straight into a Scottish winter.
"But that's behind me now. I feel settled and comfortable so I'm looking forward to the year ahead. I want to do well and help Celtic be successful."
If Celtic's season is to be deemed a success, they will want to emulate their achievements from 2012/13 - when they landed the SPL title and made the last 16 of the UEFA Champions League.
On the quest for continental glory, Rogic added: "I have the Champions League qualifiers and that will be a new experience.
"I've spoken to the players who have played in them, like the boys here at Celtic, and they all speak so highly of the competition.
"It's regarded as the best there is at club level, so it would be a great achievement if I could play my part in it.
"It would also be good for the club - and could make our season - if we could make it into the group stage again.
"We have to do our best to make sure we get there. I was at the Juventus match in the knockout phase last season and the atmosphere that night at Celtic Park was amazing."