The midfielder was a 40th minute concussion substitute in last weekend’s 3-0 win over the Toffees after complaining of feeling “dizzy” during the game.
Villa’s handling of the situation was this week questioned by brain injury charity Headway, after McGinn appeared to suffer a blow to the head just six minutes into the match.
But Smith claims the club’s medical staff followed protocol to the letter, with the Scot withdrawn the moment he complained of dizziness.
“As far as I’m concerned we handled it perfectly,” he said. “John McGinn got a whack in the face and the doctor went on after five or six minutes and he was treated for a jaw injury.
“He continued in the game having been treated for a jaw injury, when he made us aware he felt dizzy.
“That is when we decided to bring him off as we had to follow the concussion protocol.”
It is believed the Premier League, following discussions with Villa, will not be investigating the matter further.
McGinn, who missed Wednesday’s Carabao Cup defeat at Chelsea, was cleared ready to return for today’s Premier League trip to Manchester United.