The Hoops have been hailed for their display against Italian giants AC Milan in the San Siro last week but they still ended their opening Group H fixture with a 2-0 defeat.
Now new signing Pukki - who grabbed his second Scottish Premiership goal in as many games with the opener against St Johnstone on Saturday - has stressed progress in Europe's top competition will only come if dominance in open play is converted into winning results.
"We just need to work really hard to achieve second place.
"I expected to see more from Milan and see them control the game but I think we were the better team. However, the most important thing is that we did not get the result.
"You have to go and beat these top European sides because even if you play well, it doesn't give you points."
Spanish champions Barcelona are next up for Neil Lennon's men in the Champions League on October 1 but before that they face less glamorous opposition in Morton as they begin their quest to land a first Scottish League Cup since 2009.
The Greenock side visit Parkhead tonight for the third-round fixture on the back of a 2-0 defeat to Queen of the South at the weekend but boss Allan Moore says motivation will not be an issue against Celtic.
He said: "I had wanted us to be heading to face Celtic with a good run of form behind us but that is not the case. However it is a game that we do not have to lift ourselves for and that can only help."