Viorel Etko was also just unable to make the final of the 61kgs, but will now go for bronze in the repechage, as will Scottish team-mates Shannon Hawke at 53kgs and Sarah Jones at 69kgs.
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England's Sarah Grundy went through the second-chance competition of the 58kgs and has a chance to equal the bronze won by her brother Mike on Tuesday, while team-mate Sasha Madyarchyk recovered via the 61kgs repechage to also make the medals block along with Northern Ireland's Hugh McCloskey at 97kgs.
There was, though, disappointment for Olga Butkevych, Team GB's only wrestler at the London 2012 Olympics, who lost her first contest and did not get another opportunity to fight again.
Rattigan - whose wife Yana won a silver medal on Tuesday, their wedding anniversary - was looking to improve on the bronze he collected in Delhi four years ago.
After coasting through his opening bout against Angula Shikongo of Namibia, Rattigan produced an equally composed display to see off the challenge of Pakistan's Umair Tariq in the quarter-finals.
However, the 26-year-old from Manchester, whose wife said he had been unwell back at the Athlete's Village on Tuesday, could not get the better of India's Satywart Kadian, losing a bruising encounter 8-4.
McCloskey had been defeated 16-5 by Arjun Gill of Canada in their quarter-final, but will fight for bronze against Sam Belkin of New Zealand as Gill went on to reach the gold medal wrestle.
Butkevych, who had won a European Championship bronze earlier this year, lost 14-5 to Braxton Rei Stone and when the Canadian was defeated in her semi-final by India's Sakshi Malik, the chance of coming back through the repechage was gone.
Speaking just after her defeat, Butkevych said: "I probably have not just woken up yet, my body is not ready yet. I feel okay, but there is no power.
"The first match is always the hardest match, it is a proper warm-up, I think now that I am ready, so it is a shame."
Grundy won her first bout, but was then outclassed 10-0 by Aminat Adeniyi in the quarter-finals.
However, because the Nigerian, who had a bye through the first round, went on to reach the gold medal contest, Grundy was handed another chance in the repechage, where she will face Tayla Ford of New Zealand.
In the women's 53kgs, Tullibody teenager Hawke won her opening contest against fellow Scot Jayne Clason, only to then be defeated on a quick throw and pin by India's Lalita Lalita, the correct decision coming after a lengthy review with the judges.
The 18-year-old dropped into the repechage after Lalita was also victorious in her semi-final, and will take on South African Mpho Madi.
At 61kgs, Etko - the Moldova-born Romanian who moved to Scotland via London and is married to gymnast Laura Davies - had defeated England's George Ramm in the quarter-finals following impressive first-round wins for both men.
However, Canadian David Tremblay proved too strong and recorded a 10-2 win over the 36-year-old, who must now pick himself up for a clash against Malta's Adam Vella for the repechage bronze.
Ukrainian-born Madyarchyk, a Commonwealth Games bronze medallist in Dehli, lost his opening fight to impressive Bajrang Bajrang 10-0, but went into the repechage after the Indian made the final, where he fought through to the bronze contest.
Wales' Damion Arzu was beaten 12-2 by New Zealander Soukananh Thongsinh.
In the women's 69kgs class Glasgow's Jones, a former judoka, lost her opening bout against Dori Yeats.
The Canadian progressed to the final, which meant Jones could fight for bronze through the repechage against India's Navjot Navjot Kaur.