Assistant warns his players against tunnel vision, but believes recent performances away against big clubs should provide the framework for his side and points against the Gunners
According to the coach, the Dutchman is just one of many dangerous attacking options at manager Arsene Wenger's disposal, and focusing solely on the forward would be perilous.
"If you concentrate too much on Van Persie, they have three or four others who can easily destroy you on their day," Appleton told the club's official website.
"[Our defenders] have all the information they need to know about him, whether that's us talking to the players or being shown numerous videos on Van Persie and Arsenal's strengths as an attacking team."
The former midfielder believes an improved Baggies' defence should be capable of dealing with Arsenal's attack as long as they are disciplined.
"From our point of view, defensively we have looked more solid," he added.
"I think we got caught a few times against Liverpool and were naive.
"We tried to throw too many people forward where a better option might have been being more cautious in our approach instead of maybe going for one or two passes to get behind them, perhaps going for five or six passes and more build-up play.
"We've defended crosses a lot better this year, we've been better on set-pieces too, we've defended counterattacks better.
"It's more of what we do in possession of the ball and that's what we need to concentrate on this week, rather than being too concerned about what one player has done for one side."
Appleton believes recent encouraging away ties against Chelsea and Manchester United will set the table for a West Brom upset on Saturday.
After leading the Blues and Red Devils early, only to concede sloppy winners late on, he thinks, with a little discipline, the Gunners can be beaten.
"We've proven against Manchester United and Chelsea that if we apply ourselves properly, get about the field and do the right things. then we can give anybody a good game," said the coach.
History is on West Brom's side after beating Arsenal 3-2 in the capital last season, but Appleton does not think the Gunners will be too concerned.
"I'm not sure Arsenal will be too worried about what happened last season," he added.
"From their point of view they're in good form, they went to Chelsea and scored five goals.
"Then they played Marseille during the week and drew 0-0.
"They play their own way and we have to make sure we start the game better than we did against Liverpool.
"I don't see Arsenal being one of those teams who worry too much about the opposition who come to the Emirates."
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