The 20-year-old finished five-under in the tournament after carding a 72 on his final round, and was made to rue bogeys on eighth, ninth and 12th, while Bubba Watson held his nerve to claim his second green jacket.
Spieth told reporters: "It was so much fun, even if I did not show it on the back nine. Although it stings right now I will be back and I can't wait to be back. That's what's on my mind because it's tough being in this position
"I've worked my whole life to lead in The Masters on Sunday, I had it in my hands and could have gone forward with it and didn't quite make the putts and that's what it came down to.
"Hats off to Bubba. He's a deserving Masters champion this year. He played some incredible golf to make his pars down the stretch."
Spieth turned only turned professional in December 2012.