The campaign, designed to portray the self-imposed silence of some victims of bullying, includes advertisements in the press as well as on television and in the cinema.
The ASA said it had received two complaints about the press adverts, one saying that it might be copied by self-harmers, and one saying the image was upsetting to children and irresponsible.
But a spokesman for the ASA said it would not be investigating further. "It was immediately clear that the advert was intended to publicise an internet service as part of an anti-bullying campaign," he said. "We didn't consider that the advertisement was likely to cause harm or distress children."
The campaign has also appeared on television after the 9pm watershed, after initially being banned from the small screen by advertising watchdog Clearcast.