The Finnish striker hit the ground running when he arrived this summer from Schalke in a £2.2million move.
Two early goals initially appeared to pave the way for a quick introduction to the club, but since then the goals have dried up.
Pukki has had an anxious look about him in recent outings, perhaps feeling the pressure of having to deliver.
Against Partick Thistle last week he had a couple of decent chances to find the net only to allow them to slip through his fingers, but he has maintained he has every confidence in his ability to hit the mark with Celtic.
"It is still very early for me," he said. "I feel as though my form has been alright and the manager has already told me that the important thing is making sure I am getting into positions.
"I do think that the goals will come. It is a big transition to come from Germany to here and it has taken me a bit of time to adjust because the game here is so fast.
"I have really enjoyed it. The boys at the club have helped me to settle in quickly and I feel confident I will be able to get a good partnership going with Anthony Stokes.
"But when you first come to a club you know there are players who might be ahead of you and you just need to work hard and try to take the chances that you get.
"There are a lot of games coming up and hopefully I will get my chance to play my part."
Celtic take on Dundee United this weekend before preparing for Wednesday night's Champions League game against Ajax in Amsterdam.
Pukki was involved in the 2-1 win over the Dutch side when Ajax were in Glasgow and he believes there are grounds for optimism as Celtic head to Holland.
Another victory against Frank de Boer's side would tee up a riveting fixture against AC Milan at Parkhead as the Hoops bid to reach the last 16 for the second successive season, but even a draw against Ajax would keep Celtic in the running for European football beyond Christmas.
PUKKI said: "They are a very good team, they keep the ball well and they have players who can hurt you.
"But we felt as though we gave a very good account of ourselves in the game against them, just as we had against AC Milan and Barcelona in the opening two games. We know what is at stake.
"We know there is a lot that could happen depending on the outcome of this game.
"But we have to approach it the same way we have our other games and I think we are definitely capable of getting something from it."
Pukki's Finnish team-mate, Niklas Moisander, missed the first leg of the game because of injury but is now fit and could line up against his fellow countryman for this meeting.
The striker would relish the chance to go head-to-head with his international colleague, but he has stressed Celtic are determined to concentrate on domestic matters before turning their attention to Wednesday night.
And he doesn't expect the game to provide a distraction at all.
"We are all professional and we know we cannot look too far ahead," he said.
"The European games are very exciting for everyone. The fans love them and we as players love the chance to take part in them. But winning the league will always be the priority.
"I hope I am involved in both games this week. It is up to the manager."
The Champions League experience with Celtic has lived up to Pukki's expectations.
Having seen previous games on TV when he was playing with Schalke and back home in Finland, Pukki's belief that Celtic are formidable on their own turf has been strengthened now he has experienced it for himself.
"It is an amazing atmosphere inside the stadium on those nights," he said. "It does feel like a joy to be part of it.
"But when the game starts you are really concentrating hard on playing your game.
"I do think, though, that it makes people not fancy playing here. The club's record at home is excellent and they have really built a reputation for being able to cope with anyone in Glasgow.
"If we could get a positive result in the Amsterdam ArenA this week then I am sure the game against AC Milan will be an interesting one. But the most important thing just now is that we are taking it one step at a time."