Andy Robinson's men must win against England to have any hope of qualifying for the quarter-finals after surrendering a six-point lead with eight minutes remaining to lose to the Pumas in torrential rain at Wellington Regional Stadium.
Scotland collected a losing bonus point and are tied with Argentina on 10 points, while England lead Pool B on 14 points, but with their qualification not yet assured.
Some consolation for Scotland's players for their heart-wrenching loss was that qualification remains possible in six days' time against their arch rivals.
Scotland prop Allan Jacobsen said: "It's pretty low, but you've just got to pick yourself up and get on with it.
"We've got a big game on Saturday and it's cup final time for us.
"We need to get past this, recover, analyse, whatever, but we need to get ready for Saturday in Auckland.
"We're playing England in a do-or-die match in the World Cup - it's not like you have to (be motivated)."
Amid the wreckage of the loss, Jacobsen attempted to find some positives.
The Edinburgh prop added: "We did a lot right tonight. I feel like everyone gave everything and fought hard.
"I feel like we put so much in and it was not quite enough.
"We made one mistake and let them in for that try and that was the ball game."
Lucas Gonzalez Amorosino's match-winning try came amid what Scotland head coach Andy Robinson described as "30 seconds of madness".
Scotland failed to collect the restart following a Dan Parks drop goal which had handed them a six-point lead, Graeme Morrison was penalised for offside and the Pumas worked it wide where Gonzalez Amorosino rounded Chris Paterson and two covering defenders to score in the right corner.
Argentina captain Felipe Contepomi converted successfully to give his side a one-point lead.
Scotland had an opportunity to triumph, but Parks missed a drop goal one minute from time as it appeared Argentina gambled by straying offside.
Parks was forced onto his left foot and the penalty was not given, meaning Argentina survived.
Parks said: "There are different things you try in different games. You play on the edge of the law.
"I haven't seen the replay, but there certainly was a lot of pressure.
"And if you get away with it, fair play."
While the loss leaves Scotland facing elimination at the World Cup group stages for the first time, England could also exit the competition prematurely.
If Scotland beat Martin Johnson's side at Eden Park by more than seven points - the margin of defeat required to gain a losing bonus point - and Argentina claim a four-try bonus-point win over Georgia on Sunday, it will be England who go home.
It is 25 years since Scotland beat England by the required margin.
Scotland full-back Paterson said: "We've got six days to turn it round and try to beat England.
"World Cups are all about winning. We have to win next week, we have to win well next week and we'll do all we can to try and do that.
"We've got confidence that we've beaten them recently (in 2008), albeit at Murrayfield, but we hope to do it away from home and in Auckland next Saturday."
Scotland wing Max Evans called for adventure against England.
The 28-year-old Castres back, who scored in the RBS 6 Nations loss at Twickenham in March, said: "It's easier focusing already on what we need to do against England, just to take the mind off what's happened.
"We've got nothing to lose - (we should) throw the kitchen sink at them and hope for the best."
Argentina know their progression in the tournament is now in their own hands.
The Pumas will know exactly what is required of them when they tackle Georgia.
"The dream is still alive so we're very happy," said Juan Martin Fernandez Lobbe, who is set to undergo a scan on his injured knee tomorrow morning.
The number eight paid tribute to his side's attitude.
He added: "We'll keep on fighting until the end and today we got the reward, so we're very happy."
The former Sale Sharks back row also thinks Scotland can progress at the expense of England.
He added: "I believe in this World Cup anyone can beat anyone.
"And the passion Scotland has and the way they play it's going to be a very interesting match on Saturday night."
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