Much has been made of the fall-out from the Gunners' 2-1 home defeat by Manchester United last Sunday, which left them five points behind fourth-placed Chelsea after a third successive Barclays Premier League loss.
Manager Arsene Wenger was jeered by some fans for his substitution of livewire Alex Oxlade-Chamberlain for the ineffectual Andrey Arshavin.
Captain van Persie was quick to play down suggestions he had questioned the manager's judgement in an apparent negative reaction to the switch, which was made because Oxlade-Chamberlain - who set up the Dutchman's equaliser - had been hampered by a calf problem.
Van Persie went as far as to post a statement on Facebook, in which he issued a rallying call.
"There are plenty of games still left, we have recovered from reverses like this before and we will win again, so anybody writing us off is making a mistake," he said.
"This could still be a good season for us. We have the FA Cup to look forward to and the Champions League.
"We will all be giving 100 per cent to make sure we bring one of those trophies home, hopefully both of them.
"Let's all stick together and fight."
Wenger is reported to have addressed the squad ahead of Sunday's FA Cup fourth-round tie with Aston Villa to reaffirm his belief in the side.
On-loan New York Red Bulls forward Thierry Henry, whose goal beat Leeds in the third round, missed the United game with a calf injury, as did midfielder Mikel Arteta, but both could feature against Villa.
There has been some positive news on the recovery of full-back Bacary Sagna, who resumed full training with the rest of the squad for the first time since suffering a fractured right fibula during the defeat at Tottenham on October 2.
With Andre Santos, Carl Jenkinson and Kieran Gibbs also sidelined, teenage defender Ignasi Miquel has been drafted into a makeshift backline.
Barcelona-born Miquel, 19, has come up through the youth ranks at Arsenal, captaining the reserves before being handed his first-team debut in last season's FA Cup fifth-round tie at Leyton Orient.
The young Spaniard, who has been asked to operate as a make-shift left-back, is hoping an extended cup run can fulfil a life-long ambition.
"It is a dream to play at Wembley in a big final. First, we have to go step by step, but obviously if we can get to Wembley it would be a big, big thing for us," Miquel said.
"We have not won a title for quite long, so it would be great for us - but our next game is on Sunday against Aston Villa and we must focus on that.
"If we keep working and stay mentally strong we can get through it."