Scotland were unable to build on the momentum of their fourth-place finish at last weekend's Emirates Airline Glasgow 7s when they came up short in the London event yesterday.
A 14-10 defeat to France in their first game was followed by a 31-5 triumph over Portugal before South Africa inflicted a 26-12 loss to leave the Scots facing Wales in the Bowl quarter-finals today.
Victory over France would have handed Stephen's Gemmell's side a route to the Cup quarter-finals, but a late comeback was not enough to overturn the points defict.
Coach Gemmell said: "It has been a frustrating day. We had a better game against South Africa and we played some good rugby. But that game was not the game that cost us today. We did not front up against France, we made too many mistakes and suffered.
"We're not a good enough team that we can make mistakes and then not be punished for them. Our game is built on work-rate, accuracy, tempo and skills and it's disappointing that those didn't come through today.
"We can now only focus on game one tomorrow. Players know that Commonwealth Games places are up for grabs and they must front up tomorrow to be considered."
On a positive note, Scotland 7s captain Colin Gregor won his 50th cap in yesterday's competition, while Jack Cuthbert and Lewis Young won their first caps and marked the occasion with three and two tries respectively.
The hosts England sent a record Sevens crowd of 74,969 home happy after beating New Zealand 15-12 in the final match of the day at Twickenham.
England's captain Tom Mitchell kicked a late penalty drop goal to seal England's win, but the New Zealanders still capped a remarkable season of consistency by clinching the HSBC Sevens World Series with a day to spare, a 12th Series in 15 years.
England now face France in the Cup quarter-finals, while New Zealand will play second-ranked South Africa. In the other Cup quarters, Australia will play Kenya and Samoa face Fiji in an all-South Sea Island tussle.
In the Aviva Premiership, Harlequins beat Bath 19-16 to climb above their opponents into fourth place and snatch a play-off spot on a nail-biting final day.
The victory, Quins' fifth in succession, completes a remarkable comeback for Conor O'Shea's side who have also beaten Exeter, Leicester, Sale and London Irish en route to the knock-outs. They now face a semi-final trip to table-toppers Saracens.
Mike Brown's early try gave the hosts a dream start, but his effort was cancelled out by George Ford's solo effort and it was only Nick Evans' penalty that gave Quins a 10-7 lead at the break.
The second period became a battle of the kickers as Matt Banahan's yellow card prompted Quins to take a 16-10 lead and three penalties - two from Ford - left the home side just three points ahead with 10 minutes to play.
Bath pressed in the dying moments, but Ford's drop-goal attempt fell short and confirmed Quins' place in the semi-finals. In the other semi, Leicester Tigers will play Northampton Saints away next weekend after clinching third place with a 31-27 bonus-point win over leaders Saracens at Welford Road.