World Cup-holders Australia won by 64 runs yesterday to go 2-0 up in the five-match series.
But that was all overshadowed by the exit of Stokes during England's unsuccessful run chase.
In the 26th over, Stokes struck a straight drive which was stopped by bowler Mitchell Starc.
Left-arm paceman Starc then hurled the ball back hard towards Stokes who, leaning back back and turning his head away, stopped it with a hand taken off the bat.
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The relevant cricket Law or rule talks about "wilful obstruction" and does allow batsmen to protect themselves from injury
West Indian official Wilson gave Stokes out for 10, sparking the unusual sound of a chorus of boos at the 'home of cricket'.
Smith could have withdrawn the appeal.
But he saw no reason why he should and said the close-at-hand view of wicket-keeper Matthew Wade strengthened him in his original decision.
"The way I saw it, he was out of his ground, and he wilfully put his hand out -- which is the rule ... And he got given out by the third umpire," added the captain, who top-scored with 70 when batting conditions were at their toughest in an Australia total of 309 for seven.
"If you look at it ... The ball was going towards the stumps, and wasn't even going to hit him.