The 20-year old Australian midfielder produced a Man of the Match performance in the 3-1 win at Inverness with a superb assist to allow Kris Commons the opening goal.
Rogic, who joined the Hoops from Central Coast Mariners late last month, is now eyeing a consistent spot in Neil Lennon's line-up as he continues to develop with the Glasgow giants.
"I got into the club a week ago, so I can't have any complaints," said Rogic.
"But you go out every game trying to make a statement, I guess, and show him what you can do. I will keep working on the training pitch and the coach will see me every day, so I will keep going.
"It's a different style over here, so it might take me a little while before I get used to it and before I can play my best football, but I am quite happy with my first game.
"I think it was a good performance all round from the team."
He added: "Obviously a lot of players were rested.
"But I think we still had a pretty strong squad and there were some very good players guiding me through the match, which made it a lot easier."