The Australia midfielder, signed from the Central Coast Mariners in January for a reported fee of around £400,000, made an impressive debut in the 3-1 Premier League win at Inverness on Saturday.
The 20-year-old was one of nine changes made by the Hoops boss with the first leg of Celtic's Champions League last-16 clash with Juventus at Parkhead on Tuesday night in mind.
Rogic set up Kris Commons to cancel out Nick Ross' opener before goals from debutant defender Rami Gershon and Venezuelan striker Miku stretched the Hoops' lead to 18 points over second-placed Inverness at the top of the SPL table.
Lennon revealed he left Rogic out of his European squad to stay loyal to those who had got the club to the knockout stages and the Hoops new boy said: "I got into the club a week ago so I can't have any complaints."
However, Rogic, has vowed to win his way into Lennon's first-team plans.
"You go out every game trying to make a statement, I guess, and show him what you can do," he said.
"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.
"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."
Lennon's makeshift side won with relative ease which might be a bit worrying for those who are looking for more competition in the SPL.
Caley have lost their last four games, including a League Cup semi-final exit on penalties to Hearts and a Scottish Cup defeat at Kilmarnock.
However, manager Terry Butcher insists his side can get back on track against Kilmarnock on Wednesday night.
"There will be spells in the season when things go against you," he said.
"But we know we know we have the players who can turn it around.
"We are hurting at the moment because we know we should have got something from the last four matches but we haven't so we move on.
"We are still a threat, we are still scoring goals and we will always do that.
"The heads are up and we look forward to Wednesday."
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