A tweet on the company’s account linked to a video of a man entering the laundry room in his home to find a couple having sex.
The camera cut to the man’s reaction, then to the couple and then showed the man walking away looking dazed.
Then it cut to a blank screen with text that stated: "At home with your parents you’re not the boss… At giffgaff we’re all the boss." Panting sounds were heard over the video, which continued over the blank screen.
The complainant claimed the video, created by Fallon London, would cause "serious or widespread offence".
Giffgaff said it did not intend to cause offence, the ad was "humorous and playful" and there was no nudity.
The company noted that there was a warning at the beginning of the video that said: "Warning: You cannot unsee this".
It also said that just one complaint "indicated that the offence caused was not widespread of serious" as the ad had been viewed 37,530 times on YouTube at the time it provided its response.
The ASA said that although the ad did not feature nudity, it was clear that the characters were having sex.
The watchdog added that the content was available for anyone with access to Giffgaff’s Twitter feed, and would play whether or not they were signed into the site. As a result, it said the ad was "untargeted".
With regards to the warning message, the ASA said it was "initially obscured, discreetly positioned, only present briefly" and "inadequate to alert viewers to the content".
The ASA said: "We considered that the untargeted nature of the medium meant that a disclaimer was not sufficient to prevent the ad from being seen by viewers who would be offended by the content.
"Because the video featured strongly sexual content in an untargeted medium we concluded that it was likely to cause serious or widespread offence."