Victory for Rob Page's men in Yerevan and another win over Turkey at home on Tuesday would have secured Wales' place in Germany next year.
But they now need Croatia to drop points against either Latvia or Armenia to finish in the top two of Group D.
A point is also unlikely to be enough for Armenia's chances of qualifying for a first major tournament.
Even if they do not secure automatic qualification, Wales should have the safety net of a two-match playoff through their ranking in the Nations League.
But Page will rue a huge missed opportunity after a famous 2-1 win over World Cup semi-finalists Croatia last month had breathed new life into Wales' qualifying campaign.
"We're disappointed, of course, we wanted to get the win," said Page.
"We've got to pick ourselves up and finish with a performance on Tuesday.
"We look forward to finishing with momentum and if it's a playoff in March, then we take that."
Should they fail to qualify, Wales will look back on both games against a side ranked 95th in the world.
Armenia shocked the home side 4-2 in Cardiff in June - a result that put Page's future in doubt.
Wales did not learn from that lesson as Lucas Zelarayan's fine strike from the edge of the area put Armenia in front after just five minutes.
The visitors took time to find their feet and lacked a creative spark so often given to them in the past by a moment of inspiration from the retired Gareth Bale.
Only a gift from the hosts got Wales level before half-time as Nair Tiknizyan headed Connor Roberts' long-throw into his own net.
Both teams threw bodies forward in the final stages with a draw little use for either side's chances of qualifying.
But it was Armenia who looked the far more dangerous.
Vahan Bichakhchyan smashed against the crossbar, while Edgar Sevikyan's shot was turned behind by Danny Ward.
Wales move a point clear in second place in the group but can be leapfrogged by Croatia when they travel to Latvia later on Saturday.
Armenia remain three points behind Wales and travel to Croatia in their final group game on Tuesday.
