The Finland international moved to Parkhead last summer as part of a £3million switch but failed to shine.
However, after bagging four goals during the Hoops' pre-season warm-up tour of central Europe, he continued to impress after replacing injured frontman Anthony Stokes in Celtic's Champions League qualifier with KR Reykjavik at BT Murrayfield in Edinburgh.
He netted twice in the 4-0 win at the home of Scottish rugby as the Scottish champions' 5-0 aggregate victory teed up a third qualifying round clash with Legia Warsaw of Poland.
New boss Deila has been impressed with the improvement Pukki has shown since he took over.
He told the club's official website: "He was good. He had a lot of chances, including one before he scored and he just has to continue.
"He has scored in almost every game he has played now which is good.
"I've talked with him like I have talked with all the players but everything is a process.
"There will be good times and bad times during a season, but it's the dialogue between the coach and the player which is important.
"They have to be aware of what they're doing themselves, and have responsibility for their own career and development. But it takes time
"A lot of the players are listening and are taking steps but it's only been four weeks and I can't do miracles. However, we are going in the right way."