Willie Ormond's men failed to get out of their group in West Germany despite remaining unbeaten, with Yugoslavia and Brazil qualifying courtesy of a superior goal difference.
Steve McCormack's Bravehearts also went through their pool stages undefeated but will be eliminated from the Rugby League World Cup if Italy beat Tonga in the last Group C fixture at The Shay.
The Scots began their campaign with a stunning 26-24 victory over the highly-fancied Tongans but were held to a 30-30 draw by Italy, who had gained a 32-16 victory over Wales.
Although McCormack's men kept alive their hopes with a 22-8 victory over the USA at Salford on Thursday, they failed to overturn Italy's superior points difference.
That means the Azzurri only need to win by a point on Sunday to clinch a quarter-final against holders New Zealand in Leeds next Friday.
Scotland captain Danny Brough is hoping for a favour from his Huddersfield team-mate Ukuma Ta'ai, who will be leading the Tongan Haka before doing battle with the Italians.
"We've done our bit, it's now up to Tonga," Brough said. "Hopefully, Ukuma can smash a few Italians for us and help keep our amazing run going in the process.
"Everyone in the Scotland camp will be watching the game in our hotel and you can imagine what it will be like if Tonga do it.
"Games don't come much bigger than playing against the world champions and to be part of that would be absolutely amazing."
Italy will be highly motivated as they look to claim a place in the last eight in their first World Cup.
They demonstrated their battling qualities against Scotland in Workington, coming 14-0 down to earn a share of the spoils.
"It was a great comeback by us but we have got a few things to work on," said Italy hooker Ray Nasso.
"We have to win this next game otherwise we don't qualify, so it will be a big game.
"We were a bit flat after the Scotland game but we have put it behind us and now we move on to hopefully qualify."
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