Earlier Australia fired off the start to take victory in the men’s K4 1000m final, beating the Hungarian favourites before a roaring crowd.
Cawthorn, who became the first-ever British woman to medal at both the European and World Championships in 2010, finished fast but could only manage sixth.
And Cawthorn, who was the youngest competitor in the final at just 23-years-old, was disappointed to miss out on the podium but admitted the whole London 2012 experience is something she can build on.
“It just seemed to be over so quick,” she said. “I kind of got a good start and was trying to go through my race plan.
“I was probably a bit too far down at halfway so it was too much to come back. I kind of wish I could do it again – it was alright just kind of wish I could have done better than that.
“It’s good but it seems like such a long time to wait now to have another bash at it but I can take a lot away from this whole experience – it has been amazing.
“The crowd have been incredible. I was so proud of myself after the semi-finals to be putting in these performances. I think that in the final I was probably too much like ‘I know how much this race means.”
Kozak, who also won gold on Wednesday in the women’s K4, moved through the 500m field to reel in Ukraine’s Inna Osypenko-Radomska, who was looking to defend her Beijing title.
South Africa’s Bridgitte Hartley continued her sharp rise up the standings to take bronze.
In a sport dominated by European nations, Australia’s victory in the K4 final was a particular shock.
Australia finished with a time of two minutes and 55.085 seconds at Eton Dorney in London to claim its sixth gold medal of the games.
Hungary, who had been looking to add gold to the titles they won in 2004 and 2000, took the silver and the Czech Republic collected bronze.
The Australian crew fell back into their boat and punched the water in delight at their win.
In the first race of the day, Germany's Peter Kretschmer and Kurt Kuschela surged through the field to snatch victory in the men's canoe double 1,000m in a thrilling final.
The duo, who took silver at the European championships this year, passed Azerbaijan in the last 200 metres to take the title.
Andrei and Aliaksandr Bahdanovich of Belarus took the silver to add to their gold from 2008, and Russia took the bronze.
Germany fired off the start to win the women's K2 500m and deny their fierce rivals Hungary a third consecutive Olympic title.
Germany's Franziska Weber and Tina Dietze, who won silver in the K4 on Wednesday, powered away to take a half-length lead down the Dorney Lake course.
Hungary flagged in the latter stages but held on to take the silver and Poland claimed the bronze.