Now, Neil Lennon is challenging the £2.4million summer signing to deliver on a consistent basis.
The Finn scored only his fourth goal for the club when he was sent on as a second half sub in the 4-0 thumping of Hibs at the weekend.
He also won the penalty in the final minute which allowed Kris Commons to finish off Terry Butcher's side.
With Anthony Stokes completing his two-match suspension tonight when the Hoops play Kilmarnock at Celtic Park, Pukki is set to return to the starting line-up and pick up where he left off at Easter Road.
Lennon and his coaching staff have been working hard on the 23-year-old's mental strength. And the return for this investment in money and time could not come at a better time with the club stepping up its pursuit of another attacking player, Leigh Griffiths.
If Pukki is not to slip further down the pecking order, he will have to respond to Lennon's urgings to finally slot into the vein of good form which has eluded him for the first five months of his time as a Celt.
The manager was never of a mind to send him out on loan, and revealed he has felt compelled to sit down with the man he brought in from Schalke in August and reassure him he retains faith in his ability.
"I am hoping his goal at the weekend will give him a massive lift because he has definitely got traits and ability," said Lennon. "He has just not been able to piece it together on a consistent basis."
The frustration for Lennon is that, after scoring two in his first three games for the club, Pukki has taken another four months to double that tally.
Lack of confidence appears to have been the major handicap he has been struggling to overcome.
Even at Easter Road - where Pukki had replaced Nir Biton at the break - Lennon spotted that, initially, the striker was not prepared to pull the trigger.
The Hoops boss reflected: "He had an opportunity to hit one earlier in the game, but just delayed it a little bit.
"When he gets into these positions he is very, very good at cutting it across the goalkeeper.
"It was a wonderful goal, and I was really pleased with the contribution he made when he came on for the second half. He made us better."
Which is all the Celtic manager asks of anyone given the chance to wear the Hoops.
It is what he believes Griffiths will do, if Wolves agree to sell, and pepping up the attack has been the main priority for Lennon since the window opened.
However, he is also still looking to strengthen in other areas, and introducing more cover for the defensive positions remains high on his list of targets before business is concluded on Friday.
Tonight will be the final game played in this window. And, all the evidence points to Celtic already having enough resources to comfortably continue their winning streak towards another title and, perhaps, successive doubles.
Lennon is wary of complacency sneaking into the minds of his players.
The manager is quick to remind them that, though they have won their last three games with an aggregate score of 11 goals to nil to extend their lead in the title race to 15 points - the most it has been at any stage this season - they are very much there to be shot at.
He respects how much of a threat the likes of Killie's Kris Boyd can be to the shut-out record they are chasing, and acknowledges that the higher their stock rises, the more of a nasty bump awaits if they are brought back down to earth.
"We are not going to get everything our own way," reiterated Lennon. "Teams are going to come and have a go.
"And the longer the run goes on, the more the anticipation will build about how far we can extend it and who can be the first to beat us.
"We won 4-0 against Hibs, but had to earn our win.
"I didn't think at any time during the game we would be beaten, but I did think we could drop points because we didn't play as well as we have done in the previous few games."
The real test for the Celtic players will be how they react if and when they do come to the end of their unbeaten run in the league, current winning streak, and finally see their defensive wall breached.
These have been more than sideshows to deflect from the lack of European football after Christmas or any real challenge to their superiority in the domestic game.
Lennon attaches genuine merit to each and every achievement. But, do they have the drive to pick themselves back up and go again if it all comes to an end?
"It is certainly one facet that is keeping them going," agreed Lennon.
"Obviously, we want to win the title and we want to be relentless in our pursuit of it.
"But, I'm not too sure it will change that much if the run does come to an end."
If Scott Brown and Co. can keep going at the current rate, they will get over the line to secure their third successive championship with around half a dozen games to go.
If Aberdeen and Motherwell falter, they could even set a new record time for clinching the title.
But, though that would bring huge satisfaction to Lennon, and allow him to forge ahead with plans to rest players early ahead of the Champions League qualifiers in July, he has not issued any express orders to get the job done in jig time.
The Hoops boss explained: "I haven't told them I want the title won as quickly as possible.
"But I have told them to keep their standards high and their consistency - and that is exactly what they are doing."