The Gunners have lost their last three league fixtures and reports have claimed that there is increasing unrest within the dressing room.
Questions were raised over Van Persie's commitment to the club when he was visibly baffled at Arsene Wenger's decision to substitute Alex Oxlade-Chamberlain for Andrey Arshavin during Arsenal's 2-1 defeat to Manchester United on Sunday.
"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," the Dutchman wrote on his Facebook page.
"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's side take on Aston Villa in the FA Cup fourth round tomorrow.