The Scot was favourite to prevail against the IBF title holder from Namibia, but he was second best throughout the contest as Indongo prevailed by verdicts of 120-108, 118-110 and 116-112 respectively.
The 34-year-old told Sky Sports News: "He was so so awkward. He was a lot better than we thought he was going to be. He can hit as well.
"I'm going to have all the doubters saying I'm finished - but I'll come again. He started the rounds fast and the height and reach advantage meant he was out of my distance."
Despite defeat, Burns is likely to have a number of options moving forward, but with Indongo and Terence Crawford both holding two world titles apiece, he will be out of the picture at the highest level until a unification clash takes place between the pair.