The striker made a favourable, immediate impression by scoring on his away debut at Hearts and his home debut against St Johnstone last month. He has not scored since, despite starts against Morton, Kilmarnock and Motherwell. However, the 23-year-old internationalist believes "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," said the forward signed from Schalke.
Pukki, who played for Sevilla, knows that integration at a club demands patience.
"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," he said. "It's not for me to say how long this will take but I'm confident it will work out."
He added: "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."
His bedding-in period may be helped with a chat with Mixu Paatelainen, the Finnish manager, who played for six Scottish clubs - Dundee United, Aberdeen, Hibernian, St Johnstone, St Mirren and Cowdenbeath.
"He has been watching our games," said Pukki who played in the national team's 3-0 defeat by France this week. "He was able to give me some advice and that's always helpful because he knows the game over here. I'm aware that he was a hero at Hibs as a player and now we go there this weekend."
Pukki maintained he was happy in Scotland, adding: "I have played more than in Germany and the team-mates have been very welcoming. The quality of the football here is better than people say."
He is anxious to make an impression so that he can start his first Champions League group match for Celtic after coming on against AC Milan and Barcelona.
"Their draw with Milan showed they are a good team," said Pukki of the Dutch opponents. "They have a Finn at centre-back - Niklas Moisander - and I know he's an excellent player. I hope I can play against him and score some goals."
He is, however, still searching for recognition at home and abroad. "Football is getting bigger but ice hockey is still the biggest sport back home," he said. "But we are an improving national side and if we can reach the next Euros then, hopefully, it will give the sport another boost."