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The 29-year-old hurdler helped Team GB surpass the 65 medals won at London 2012, and Scotland's Olympians equal their best ever medal tally of 13.
She also joined Yvonne Murray as Scotland's most decorated track and field athlete with an 11th major medal.
"It just means the absolute world to me," Doyle told BBC Scotland.
"I wanted to come here and take something back. We knew we were capable of winning a medal but it is one thing being capable of it, another thing going out there and doing it.
"I couldn't have done it with a nicer bunch of girls as well.  I am over the moon that I can now call myself an Olympic medallist.
"I have got Commonwealth, Europeans and World Championship medals so to have an Olympic medal to add to the collection is amazing."
Doyle, who finished eighth in the 400m hurdles final, clocked 52.4 seconds for the lead-off leg before Anyika Onuora, Emily Diamond and Christine Ohuruogu took GB to bronze, behind the United States and Jamaica.
"My job was done early so I just had to sit and watch," she added. "By the time it got to Chrissie I was just screaming, but I had complete faith she'd get the job done.
"It is great to be part of such an amazing GB team - absolutely fantastic."
Doyle was the first Scottish track and field athlete to stand on an Olympic podium since Liz McColgan (women's 10,000m silver), Elliott Bunney (men's 4x100m relay silver) and Murray (women's 3,000m bronze) in Seoul in 1988.
Doyle's medal was one of several notable Scottish performances on the final night of athletics.
Andrew Butchart, in his first major championships, took nearly five seconds off the Scottish 5,000m record of 13.13:30 he set in late May, setting a new mark of 13.08.61 in finishing sixth behind double gold medallist Mo Farah.
"I am over the moon," the 24-year-old from Dunblane told BBC Scotland. "The place is more important than the time, but I will take the time.  I am so happy.
"I came into this year being really positive, and I guess I showed that.  I am not scared of anyone, no matter who they are, and I think everyone has to be like that.
"You can't fear these people.  I train and work as hard as them so I deserve to be there.
"I have no idea what I could do next, but it is looking good.  This is my first majors and it went really well.  I just hope I can keep going and progressing."
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Lynsey Sharp continued her strong form in Rio as she set a new personal best of 1:57:69 to finish sixth behind gold medallist Caster Semenya in the women's 800m.
"I have run faster than I have ever done before after three rounds, in a very competitive field, so I can't be too disappointed," the 26-year-old from Dumfries told BBC Scotland.
"It is the nature of the sport that you will be disappointed unless you get a medal, but I always knew that was going to be a big ask in a really competitive field.
"I will see how my coach says I ran but I have got to be happy. I finished quite strongly and felt like that was my best chance - to pick people off in the last 100m.  It was good."
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A summary of the above article is?
Scot Eilidh Doyle admits she is "over the moon" at winning an Olympic medal after helping Great Britain's women take bronze in the 4x400m relay in Rio.