Organisers of the League Cup competition, now sponsored by the energy drink, will make the third-round draw in China – so it will be at 4.15am on Thursday, British time.
EFL chiefs have defended the decision, but Wagner says that while he understands the reasoning, he would make it more suitable for fans.
“I can only go from my own experience in Germany, where the Cup draws are always something very exciting,” said the Town boss, whose side have to overcome Rotherham United tonight to make the third-round pot.
“Usually the whole family is in front of the TV to see which team you get drawn against.
“At 4.15 in the morning it is difficult for a lot of people to watch it.
“There are reasons why this has been done and we all together know that this is about money.
“We, me included, get paid by money so I think it makes no sense to moan about it.
“On one side we like to see the greatest players and the greatest teams and this costs money, and this is the reason why this happens (the draw being made when it is).
“If I could decide it, I would say show it at a better time than four o’clock in the morning, but I only think we have to accept it and carry on.”
The third-round draw is scheduled to be made at approximately 11.15am local time, but the time difference with China means supporters of the clubs involved will have to be awake very early to see it.
It is the latest controversy to hit the rebranded League Cup competition this season.
The first-round draw, held in Thailand where the makers of energy drink Carabao are based, showed Charlton playing two teams in the on-screen graphic.
Then former England winger John Salako, conducting the second-round draw, got confused about which teams were playing at home or away.
Yet those mishaps are not behind the EFL’s decision to keep the third-round draw from public view. Instead, it claims the move is part of its plan to boost exposure in Asia.
A spokesman said: “We understand that not everyone will agree on the timing of this week’s round-three draw, but in staging it this way it will give the competition both the maximum exposure in the UK, Chinese and South East Asian markets.
“This is not only an important factor for the EFL but also our new sponsors Carabao, who, like ourselves, plan to use the growing global appeal of the competition to reach new audiences.
“Once the logistics have been completed in Beijing, the UK will be waking up and the breakfast media will be able to report and get reaction on the 16 ties that will take place next month, which we feel is an interesting move away from the usual post-game evening draws.
“The round-three draw itself is not being televised live in China or anywhere else but the EFL will be providing full coverage across its Carabao Cup twitter feed, with news and reaction as it happens.
“Our decision to go to China is part of a strategic plan to grow the EFL internationally and specifically boost profile and exposure in ASEAN markets.
“A number of potentially significant meetings are being held around the draw that we envisage will deliver a benefit to all 72 clubs of the EFL.”
The seven Premier League clubs who qualified for European competitions enter the draw at the third-round stage, including holders Manchester United.
The majority of the second-round were last night, with six ties – including Town at home to Rotherham – taking place tonight.