The retailer received two complains about two ads - a YouTube pre-roll and a web page about two bundles which clocked in at £149.99 and £299.99 respectively.
The shoppers challenged the brand because they were told the consoles were out of stock when they tried to purchase them on 29 September last year, the same day they viewed the ads.
Argos supplied the watchdog with spreadsheet showing demand v supply for the two bundles during the week of the promotion and the six weeks preceding it, saying they had been able to meet around 84% of buyer demand for the bundle.
The shopping giant added that the deals advertised in ad were made available to consumers the previous day, 28 September, and had created "enormous demand" not only for Argos but also for other retailers. The company added that a 27-fold increase in demand showed it was a genuine case of being caught out by unprecedented interest.
The ASA disagreed, saying the ads depicted the promotional offer with "no indication that availability was limited," and that because Argos didn't provide sufficient evidence as to how it had estimated what the promotional demand was likely to be it was in breach of the code.
"We noted that the ads would have finished their run," read the regulator's rulling. "We told Argos to ensure that, for future promotions, it was able to demonstrate that it had made a reasonable estimate of likely response and either that it was capable of meeting that response or would provide consumers with sufficient information to make an informed decision on whether or not to participate."
The caution comes just weeks after John Lewis was rapped by the ASA for an "unfair" Black Friday Apple Watch promotion.