Jackson suffered a second defeat in a major event by a rival who got a "false" start as the rain came down in Africa.
Javelin thrower Steve Backley provided the only British winner on the final day as he completed a cup hat-trick, while American superwoman Marion Jones proved she was human after all as her year-long unbeaten record was ended.
The Great Britain men, minus key injured performers like Jonathan Edwards and Doug Walker, finished sixth as hosts and title holders Africa took the Cup, renamed after Nelson Mandela, by just one point from Europe.
"We are not disappointed," said team director Max Jones. "We estimated that we'd get 89 points and that's what we got. It's just a pity we could not have a full-strength team here.
"But, if you'd have told me a year ago that this season we would win the European Cup, finish top of the medals table at the European Championships and qualify for the World Cup I'd have been delighted."
Jackson, who has insisted the decision to withdraw from the Commonwealth Games in Kuala Lumpur to run in Japan instead was not money motivated, lost out on the winner's prize money.
The 31-year-old Welshman was beaten into second place by just 0.01sec after Germany's Falk Balzer got a flier to win in 13.10. Balzer's reaction time, and the even quicker one of Rod Zuyderwyk in the lane alongside, should have forced the starter to bring them back.
"The starter has control of the race and if he doesn't call-us back you just have to accept it," said Jackson, who lost the world indoor title in Toronto in 1993 when local hero Mark McKoy also beat the gun.
Jones said: "We protested but were told the starter didn't hear the false start bleep maybe because of the crowd noise."
But there was no stopping Backley as he pocketed the top prize with a second round effort of 88.71m to break the Cup record set six years ago by injured rival Jan Zelezny.
"That feels very special," said Backley. "It's my third World Cup title - though the first one I have been paid for.
"I felt under pressure a bit out there because the team needed the points. But I think we have all done ourselves proud because we did have a slightly weakened team."
Britain's one-lap relay quartet of Mark Hylton, Jamie Baulch, Sean Baldock and Iwan Thomas had to settle for second despite a storming last leg from Thomas which made up two places. The United States won in 2:59.28 as Britain, who clocked 2:59.71, were left to rue Mark Richardson's decision to pull- out of the squad to concentrate on next week's Games.
Cardiff's Doug Turner sharpened up for the Commonwealths by clocking a season's best of 20.51sec in the 200m, which was won by Namibia's Frank Fredericks in a Cup record 19.97.
Jones tasted defeat for the first time in 39 competitions - stretching back to 6 September last year - when she had to settle for second in the long jump as she attempted to follow-up her victories in the 100 and 200 metres.
But Jones only managed a jump of seven metres in the stadium where many had forecast altitude could see her soar to around 7.50m and lost out to the 7.07m leap of Germany's Heike Drechsler.