Stroud was forced to issue an apology after wrongly awarding Burton Albion a free-kick after Dwight Gayle encroached into the box before Matt Ritchie struck a first-half penalty.
The Bournemouth official should have ordered the spot kick to be retaken.
Ritchie netted after the break to give Newcastle a 1-0 win and send the club back to the top of the Championship.
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The decision infuriated Benitez and his players, though United's manager chose his words carefully after the game.
Stroud consulted Hartlepool-based fourth official Tony Harrington in the minutes after his initial decision, which was greeted by incredulity by Ritchie and his team-mates.
And Sky Sports are now reporting that Stroud will not officiate at Gillingham this weekend in the wake of the error.