The Finnish forward has slowly begun to settle into life in Glasgow, but has still looked a little anxious at times on the pitch, despite getting his Celtic career off to a decent start.
Pukki scored two goals in his opening two games but he believes that he still needs time to adjust to his new team-mates - and they to him.
"Of course I can't be like Gary or anyone else - I'm me," he said. "I hope I can do well and people will talk about me and only me.
"I've been here for one month now and I'm happy that I managed to score a couple of goals in the first few games.
"I've had some matches now without scoring but I'm sure that the goals will come.
"Everything is still quite new and it will take time for me to fully adapt, but I have time on my side.
"The hardest thing to get used to is new team-mates. I have to learn how they play and they need to get used to my style.
"It's not for me to say how long this will take but I'm confident it will work out.
"It felt good when the fans chanted my name - that's encouraging.
"When I moved to Schalke it took me a few months to settle.
"I scored in the early games but you still need to get used to everything at a new club."
Celtic play Hibs at Easter Road this afternoon before preparing for Ajax in the Champions League on Tuesday night.
And Pukki would love the chance to get a crack against the Dutch champions - and one over his fellow-countryman Niklas Moisander.
"It won't be easy," he said. "Their draw with Milan showed they are a good team.
"They have a Finn at centre-back - Niklas - and I know he's an excellent player. I hope I can play against him and score some goals.
"I didn't get a chance to catch up with him last week as he missed the internationals through injury.
"I think he will be ready for the game next week.
"It might give me an advantage to know how he plays - but he will say that it gives him an advantage to know all about me! We'll see how it works out."
Having moved from Schalke, Pukki already feels relatively settled off the pitch.
And he has also insisted that the standard of the SPFL is better than many give the league credit for.
"Of course I have played more than in Germany and the team-mates have been very welcoming," he said.
"The quality of the football here is better than people say. You have time for yourself when you get the ball and I'm fitting in well."