Because you identify as being from AZ, I'll assume that's where this happened. Please say so if that's not correct.
I only lived there for 4 months and I'm certain the carpet was thoroughly cleaned and stainless upon moveout - though I foolishly did not take photos.
Do you have any witnesses to the condition of the carpet when you moved out? Professional movers, or friends who helped you move? Did the letter you received include a description of the supposed damage to the carpet, and/or photos, or just a "carpet replacement - $X" line item?
Not having taken move-out photos doesn't doom you, it just makes winning your case less of a slam-dunk than it would have been.
There was also no walk-through move out inspection, which I thought was odd.
Under Arizona law the tenant has the right to be present at the landlord's move-out inspection, but to exercise that right he or she has to request to be notified of when that will occur. Here's a link to the security deposit section (ARS 33-1321); the wording is in paragraph C.
How do I go about this? Do i have any chance here?
If you want to dispute this, your first step would be to write them a letter in reply. If the landlord failed to send the accounting by the deadline in paragraph D of ARS 33-1321, then you can certainly discuss that in your letter. If they met the deadline then you'd just tell them you left the carpet clean and undamaged, and if they don't send you your security deposit back within, say, 2 weeks (pick a reasonable amount of time) you intend to sue for the return of your deposit in small claims court. I'm guessing your security deposit did not exceed the $3500 AZ small-claims limit - ?