Australia's 2-0 loss away to Japan last week put their qualifying hopes on a knife edge.
They need to beat Thailand in Melbourne on Tuesday then hope Japan can hold Saudi Arabia to a draw or better in Jeddah to grab the second direct berth to next year's tournament in Russia.
Australia can still qualify from third place but would need to negotiate home and away playoffs against the third-placed team in the other Asian group then a side from the North, Central and Caribbean (CONCACAF) region.
"Going to consecutive World Cups has been very important not just for the national team but for Australian football, the A-League and lower leagues," Milligan, who led the side in the defeat in Saitama in the absence of regular skipper Mile Jedinak, told reporters.
"I still truly believe that we will go out Tuesday night and we'll put in a good performance. Whether it's Wednesday that it's announced that we're going to a World Cup or whether we have to wait a bit longer, it will happen.
"Obviously that's worst case scenario but there's a long way before we have to hit that panic button."
Australia have never been a side renowned for pace but they were made to look sluggish by fleet-footed Japan, whose well-organised defence scrambled hard to frustrate the Socceroos' forwards.
Thailand, already eliminated from the World Cup running, are unlikely to offer as stiff a challenge as Japan but Australia need to accelerate their ball movement forward, said winger Mathew Leckie.
"The ultimate topic we spoke about (after Japan) was that the ball movement was too slow," he said.
"We let them get back into their formation and sorted in their own half very easily.
"If we moved the ball quicker and went forward faster we could have definitely found gaps.
"If we can get on top of Thailand push them back into their own half, it'll definitely give us the opportunity to get high.
"We need goals and towards the end of the game we might have to take some risks as well."
(Reporting by Ian Ransom; Editing by Greg Stutchbury)
