The Spaniard has come under fire recently after seeing his side lose 1-0 against Sheffield United at Bramall Lane on Monday in the Premier League, continuing their struggles on the road.
They followed that up with a 3-2 win over Portuguese side Vitoria in the Europa League on Thursday, but went behind twice before Nicolas Pepe salvaged a result with his late brace.
Van Persie, who starred for Arsenal under Arsene Wenger from 2004-2012, was asked if he thinks the north London side have improved since the Frenchman’s departure.
"I don't think so,” he told BT Sport.
"I don't think that Emery really connects with his players. I think they're still weak on set-pieces – that was back in my time still a problem, to be honest.
“Everyone should feel responsible. Do you play zone or do you play man-on-man?
"I think when you're struggling you should play man-on-man, because then you just pick your man then you are responsible for your man. It's a one-on-one fight.
"Last weekend they again conceded from a corner kick. I said it a couple of weeks ago as well, Arsenal lose 12-15 points per season by set-pieces and that should stop. You have to sort it out, you have to find a way.
"You can see some players, and it's not honest to judge the coach based on tonight, it's based on the last couple of months and even the year before.
"As a player, you want to have that feeling you have to sprint back, and now you see a couple of players that jog back. There's a danger there.
"If you have a very strong coach, and you're in midfield, and you see there is danger somewhere, you will sprint for your life, because you know if you don't do it you get punished."
But Van Persie believes the manager lacks clarity in the messages he’s sending to his players.
“I've had Wenger, Louis van Gaal, [Sir Alex] Ferguson, so many coaches,” he said.
"Their main quality was to be clear. If I'm really honest, someone sent me a video of him [Emery] last week trying to explain something, and I couldn't figure out if he was saying 'come, come' or 'come!'.
"That is very important. You have to be clear, you have to be the leader and the leader needs to be clear towards his players."
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