With Villa losing 3-2 late on in the match, the World Cup winner went up for a corner in the hopes of helping his side find an equaliser.
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However, Arsenal were able to hit them on the break and score a fourth goal to seal the 4-2 win, with Martinelli tapping into an empty net.
Following the defeat, ex-Arsenal boss Emery was far from pleased with former Gunners goalkeeper Martinez's decision to go up for the corner.
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Speaking exclusively to talkSPORT, he said: "Our game plan is, of course, quality really and on the pitch they have to take the decision.
"He decided in the last action to go to the corner offensively, but I don't like it.
"But I told him nothing, before or after because in all my career I have never told our goalkeepers to do it and the statistical data is going against the teams that are going with the goalkeeper more than scoring any goals."
When asked if he has told the goalkeeper not to do it again, Emery replied: "He can learn for the next matches."
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Villa's first half showing would have led many to believe that they would go on to beat the Premier League title chasers.
Ollie Watkins' opener was cancelled out by Bukayo Saka's volley, but a neat finish from Phillipe Coutinho put them ahead at the break.
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Arsenal levelled the scoring through Oleksandr Zinchenko and thought they would drop further points following Martin Odegaard's miss.
However, a Jorginho strike from range in stoppage time hit the underside of the bar and went in off Martinez.
Martinelli's finish five minutes later sealed a dramatic win for the Gunners to put them back at the top of the Premier League table.