After just two games, the Finnish hitman has already scored more than a quarter of his total for his entire first season at the club.
But he insists he does not feel under any pressure to keep his flying start going because he is floating on air due to the confidence shown in him by manager Ronny Deila.
Virgil van Dijk scored the opening two goals against the Icelandic champions to set up Celtic for a 5-0 aggregate win, but it was the clinical finishing from Pukki which was the highlight of the performance at Murrayfield watched by 36,000 fans.
Now the man signed for £2million from Schalke last summer wants to use this as a launchpad, and will burst a gut in training to get up to the level of fitness he knows is required to make this happen.
He said: "I know what the manager means when he says I can give more because I am not quite fully fit yet. There is work still to do, and I will be sharper and faster when I am completely fit."
Pukki is grateful for the chance to edge closer to his peak by playing in the first team. And he is desperate to repay Deila for the faith he is showing in him.
He said: "It is a big thing to have his support. It gives me confidence that he believes in me."
However, Pukki is only too aware that, with Anthony Stokes due back from his thigh injury this weekend, he has to keep his form going - especially in front of goal (he also scored four goals in pre-season) - or he will be back on the outside looking in as Celtic's season picks up pace.
His scoring exploits have left him better placed to deal with these demands, and he said: "There is no pressure on me. I am enjoying playing now, and I hope I can keep going. I believe in myself."
Pukki's immediate aim is to ensure he retains his starting place for next week's Champions League third qualifying round tie against either St Pat's or Legia Warsaw.
Deila will attend tonight's game in Dublin between the pair to get an up-to-the-minute gauge of whichever side his team will face.
Pukki will also try his best to get a look at the game. But, he admits he already hopes that it is Dublin he is heading to for next week's first-leg tie.
He said: "I haven't seen either of these teams play. I think Legia would be the harder to play against. But we will see what happens."
Pukki also hopes Fraser Forster will still be in the Celtic side when the remainder of the qualifiers take place.
Like everyone else in the dressing room, he is aware of Southampton's failed bid to land the keeper.
But he also knows how important the Englishman is to the Hoops, and said: "He is one of the best keepers in the world, so it is important for us to keep him.
"He showed last year that he is a very important player for this club. Many teams are after him, but I hope he stays."