Arteta dubbed the 1-0 triumph as the best of the season as Arsenal went four points clear at the top of the table.
Parlour told Tribalfootball.com: "I think Palace, they've had such a great start, haven't they? They're really dangerous. I know they lost in the week, but they've made a couple of changes. They're really well organised. I really like their manager. I think (Oliver) Glasner's done a great job at Palace. He really has. Well organised, hard to break down.
"You've got (Jean-Philippe) Mateta who's in great form as well. So it was always going to be a difficult game. And obviously, when you're playing on a Sunday and you know one of your rivals, Liverpool, have lost already, you've always got to try and I know Man City were playing at the same time.
"They didn't know what the result was. But you've just got to win your football matches and hopefully other teams will do you a favour, which is what happened this weekend. After seeing the Man City result, I should imagine they thought, 'well, this is a big weekend for us because two of our big rivals have lost and we've won'.
"So we've gained three points in the Arsenal way and you can't afford to lose too many games in a season. And I think Liverpool now, four or five they have lost, haven't they? Four games, I think, they've lost. It's not ideal for Liverpool at the moment and I don't know what's gone wrong now. But Arsenal, all they've got to do, it's an old cliche, but just one game at a time, just win your football matches and hopefully other teams do you a favour around you."
Bookmakers don't get it wrong
On how Arsenal's title chances now appear, Parlour smiled: "Again, the bookmakers don't get it wrong too often.
"I'm sure they're heavy, heavy favourites to win the league now. And they've just got to keep going. Not think about the league, but just keep trying to win football matches and sooner or later they'll get the job done."
- Ray Parlour was speaking to Tribalfootball on behalf of NetBet Online Casino