During the final, team management became concerned and coach Stephen Kearney convened a meeting of the whole group in London after the match, inquiring about the insipid display in the decider, lost 34-2 to the admittedly near-perfect Australians.
Several players were questioned about sleeping pill use which may have led to diminished performances.
The New Zealand Rugby League is investigating the issue as part of a review of the unsuccessful defence of the World Cup.
The link with energy drinks and pills came after the team had instigated an alcohol ban - driven by the players - before the quarter-final against Scotland. It was meant to ensure players were in peak condition for the final stages of the tournament but some players may have found alternatives to alcohol.
What is not clear is whether the drinks-pills use continued after the first meeting following the quarter-final, when the three players were 'named and shamed'.
Unconfirmed reports suggest that up to five Kiwis were questioned about the use of the substances in the meeting after the final but it is not known whether the original three were part of that five. However, it is known that team management noticed a lack of mental alertness in some players.
The Herald on Sunday understands every member of the Kiwis squad were given a sleeping pill for the flight to the Northern Hemisphere, while players were also offered pills during the first two nights in the United Kingdom to help adjust to jet lag and sleep patterns. Beyond that, medication was given out only occasionally to deal with genuine sleeping problems. Kiwis management now believe players sourced pills from friends in the UK, and may also have had some supplies from family before they left for England.
Concerns about the misuse began to surface when some team-mates noticed some players looking "dozy".
"They looked like they had a prolonged hangover," said one source close to the team, "and were confronted by their team-mates who thought they had been drinking all night."
The issue came to a head after the quarter-final when, in a exclusive meeting of the playing squad, three players were questioned in front of their team-mates. However, further suspicions were raised after the final, during which the Kiwis barely fired a shot.
"Some of the players looked half-asleep," said one observer. "The mental alertness just wasn't there; they looked like zombies, and their body language was all wrong. At one stage, one player [during the final] looked dazed - like he had been tackled or just made a tackle - but he hadn't even been hit."
In a tense meeting after the final, Kearney demanded to know what had happened. The NZRL review is set to conclude next month.
"I became aware of this issue after the tour," NZRL chief executive Phil Holden told the Herald on Sunday.
"I'm hugely concerned from a player welfare point of view - that is the primary issue. It's a misuse of prescription medicine and we are gravely concerned.
"We also need to find out how and why they are using it and need to find out how extensive it is. And we want to know how they are sourced - as from a Kiwis' point of view pills were only given out occasionally to players with sleeping problems.
"It is important for us to take a leadership position in this area. [In the future] we [will] need to put the appropriate measures in to safeguard the players and protect the organisation accordingly.
"We don't know what that will look like at this point in time but we need to make sure there is a robust education and support program in place to make sure that people understand what is going on."
