Victory over the former Asian champions would guarantee a third consecutive FIFA World Cup appearance for the Socceroos, who lie in Group B's second automatic qualifying spot and a point ahead of third-placed Oman with one game left.
But despite last week's emphatic 4-0 win over Jordan, which included Neill's first goal in 91 appearances for Australia, the veteran ex-Premier League defender said no one was celebrating prematurely.
"It's very calm. The manager and the senior players have made sure no one's talking about dancing the samba. Nobody's in Brazil yet," said Neill.
"We need one game, one win. Then we can start thinking about all the dreams coming true."
But coach Holger Osieck also warned against complacency heading into the last group game in front of 80,000 fans in Sydney.
"I am pretty sure we are going to have a pretty good game tomorrow," Osieck said.
"Everybody is 100 per cent focused, we're going to have a great crowd, we play at home and I think there are so many motivating positives, so I'm pretty sure it's going to happen."
For many of the ageing Socceroos, a victory against Iraq represents their last chance to play in a FIFA World Cup.
Australia's most capped player Mark Schwarzer will be 41 come next year's showpiece, while Neill, striker Tim Cahill and midfielder Mark Bresciano - who will all be 34 or older by then - are also desperate to qualify.
"We really would love to play this World Cup together because it's been such a great adventure being part of the Socceroos for so long," Bresciano said.
"For me personally and some of the other boys we'd get to play in three World Cups if we get a result on Tuesday so it would be a massive achievement for a lot of us."
Japan have already qualified as winners of Group B, leaving only one automatic spot vacant. The third-placed team go into a play-off series.