Newcastle beat the Gunners 1-0 at St James’ Park on Saturday after Gordon scored from close-range.
The goal was allowed to stand after a lengthy VAR check that reviewed whether the ball had gone out of play, for a possible offside and a potential foul in the build-up.
The decision infuriated Arsenal manager Mikel Arteta who said it was "a disgrace", which was "embarrassing" and made him feel "sick".
Arteta also questioned whether the Premier League was "the best in the world" after a succession of recent officiating errors.
In a statement, Arsenal said the club "wholeheartedly supports Mikel Arteta’s post-match comments after yet more unacceptable refereeing and VAR errors."
"The Premier League is the best league in the world with the best players, coaches and supporters, all of whom deserve better,” the statement added.
"PGMOL urgently needs to address the standard of officiating and focus on action which moves us all on from retrospective analysis, attempted explanations and apologies.
"We support the ongoing efforts of Chief Refereeing Officer, Howard Webb and would welcome working together to achieve the world-class officiating standards our league demands."
The PGMOL have yet to comment.
