You defend the slant by playing man coverage and not giving up inside position to the receiver. The phrase "second defender" when used to refer to the sideling applies. Force the receiver outside in close man coverage. It seems to me that Perry was so concerned about the long ball that he felt it was a big enough threat to run a mid-deep zone all game.
Had he put his corners on the line to jam the receivers and stick to them in man, while leaving safety help over the top, the slant would not have been nearly as effective. We would, however, have been more succeptible to deep passes and the safties would have had to be on their game.
I'm convinced that playing man and possibly giving up long pass plays would have been a much better risk/reward equation than allowing AZ to dink and dunk their way down the field and chew up the clock, and not stopping them anyway.