The promising youngster impressed during the Gunners' 2-1 loss to Manchester United yesterday and was awarded a standing ovation on his departure from the pitch.
"It's nice when you know the crowd are on your side," said Oxlade-Chamberlain.
"I can only repay them by working my hardest when I do get on and trying to impress them.
"But, ultimately, it's putting a shift in for the lads for the club and for the manager. So I'll continue to do that when I'm playing."
Chamberlain joined Arsenal from Southampton in the summer.