Team GB were told they had won a silver medal in the mixed relay triathlon, before their result was downgraded to bronze.
Initially, it was thought Potter had snatched silver, only for this to be amended.
“We were told second, we were given second and then it all of a sudden changed but, no, we’re just super happy to have these medals around our neck,” Georgia Taylor-Brown told Eurosport.
“We all put in great legs there and, we had plans individually and we committed to them and it obviously paid off”, she said.
“Super proud, the team did such an amazing job,” he said.
“Couldn’t have asked for a better team today. We all went out there, we fought for every second and this is where we ended up and we’re amazingly proud of it.
“Really proud to bring back a bronze for Team GB and kudos to Sam, what an amazing third leg.”
Taylor-Brown was caught by the German team during the running section of her leg, before Sam Dickinson regained an advantage for Team GB as he handed over to Beth Potter for the final stint.
A strong swim kept Potter ahead, but she was caught by American Taylor Knibb and Lindemann during the cycling and running sections of her leg.
After receiving their bronze medals, Dickinson said: “Hopefully the winner was triathlon today and we’ve inspired the next generation to get into it.
“Hopefully we have a bunch more people doing swim, bike and run.”
The triathlon events in Paris have been overshadowed by the side story surrounding the water quality of the River Seine.
Potter has insisted the controversy has not affected the team’s preparations.
“We’ve all coped with it really well and you have to respond to the situation you have on the day and as long as you stay calm then we were all good and I think we did that really well,” she said.