Ireland's hopes of qualifying for the World Cup Sevens Plate competition were dashed when they were beaten 28-5 by Russia in their final match to finish fifth in Group A.
They will now compete in the Bowl event - for teams that finished fifth and sixth in their group - where their quarter-final opponents will be Chinese Taipei.
"The players are very disappointed at missing out in the final game," said skipper James Topping, who gave his side an early lead against the Russians.
"Our aim was to get into the Plate, but we have to settle for the Bowl again.
"But all credit to Russia. They were the better team on the night and just stopped us playing the rugby we wanted to against them."
Ireland had resumed their challenge on Saturday with a draw against Korea before losing 33-12 to the hosts after a brave fightback from an early 19 point deficit.
Argentina, who finished second in the group to defending champion Fiji, will meet South Africa, beaten finalists in the last worlds four years ago, who were easy winners of Group B.
Fiji will face Canada, one of only two representatives from the Northern hemisphere, in the opening quarter-final of the Melrose Cup.
The Fijians looked in awesome form as they trounced Kenya (52-7) and Korea (33-7) to top Group A with a perfect record while Canada qualified from second place in Group B.
New Zealand, who had Rush taken to hospital with a feared broken leg, will meet Samoa in the final quarter-final.