The duo, who only teamed up 18 months ago, needed to finish ahead of their New Zealand rivals to claim gold.
But after a strong start, a change in wind direction caused them to drop off the pace and they never recovered.
The Brits ended up finishing ninth, while their Kiwi rivals Jo Aleh and Olivia Powrie took first place to claim the country’s first gold on the water at London 2012.
Mills and Clark were both initially upset that they ‘hadn’t brought the fight to the race’, but then the reality began to sink in that they had matched their male counterparts Luke Patience and Stuart Bithell who won silver just an hour or so earlier – and taken the honour of being the first British women to win an Olympic 470 class medal.
Cardiff born helm Mills, 25, who lives in Rodwell , said: “We were both absolutely gutted, I just felt I’d let everyone down and got a bit emotional.
“Sport’s hard, the margins between winning and losing are tiny, we made a tiny mistake and got punished hard, from then on there was nothing we could do and that’s hard to take sometimes.”
Mills said in hindsight they should have tacked and followed the Kiwis into clear air but added: “Hindsight’s a great thing.”
Two-time Olympian Clark finished sixth at the Beijing 2008 Games with Christina Bassadone and then teamed up with a variety of helms before beginning a London 2012 campaign with Wey-mouth’s double gold medallist Sarah Ayton .
But when Ayton retired from the sport to concentrate on motherhood, Clark said rising star Mills was the obvious choice for a teammate.
“But Hannah’s a legend, when we started sailing together 18 months ago we put everything in and we weren’t even thinking about medals.
“We teamed up in Feb-ruary 2011 and were scrapping it out to get selected, there was a three-month window of opportunity to make that happen.
“We did it and went from strength to strength.”
Clark, 32, said after being the first British women to win the 470 World Championship title in May this year she was delighted to have made history again.
Mills said the moment had been made even more special by being able to share it with the family and friends who gathered on the Nothe spectator site.
She added: “We’ve done it for ourselves and for our family and friends and no other reason than that. I want to enjoy the moment.
“Hopefully we’ll look forward to the next opportunity in Rio, sort ourselves out and win gold instead.”