The 36-year-old rapper joined Madonna on stage with US rapper Nicki Minaj and was performing the cheerleader themed "Give Me All Your Luvin'," off Madonna's latest album when M.I.A. extended her middle finger in a fleeting obscene gesture while facing the camera.
NFL spokesman Brian McCarthy said in a statement that was NBC was to blame for a technical failure.
"There was a failure in NBC's delay system. The gesture in the performance was completely inappropriate, very disappointing, and we apologise to our fans," he said.
NBC sports spokesman Christopher McCloskey shifted more of the blame back to the NFL, saying, "The NFL hired the talent and produced the halftime show. Our system was late to obscure the inappropriate gesture and we apologise to our viewers."
Madonna was the first female Super Bowl halftime headliner since the notorious Janet Jackson "wardrobe malfunction" of 2004, during which fellow performer Justin Timberlake tugged at her costume, exposing her nipple to millions of TV viewers and causing an uproar.
Sunday's Superbowl broadcast, traditionally the most-watched single event on US television, drew a slightly lower audience for the New York Giants 21-17 victory over the New England Patriots than last year's record breaking 111 million viewers, according to preliminary figures.
According to overnight Nielsen ratings, the game drew a 47.8 household rating, slightly down on 2011's 47.9 household rating.
The Parents Television Council said on Monday both the NFL and NBC were to blame for the M.I.A. incident and asked for further immediate steps to be taken "to hold those accountable for this offensive material."
"The network cannot say it was caught off guard. It has been eight years since the Janet Jackson striptease, and both NBC and the NFL knew full well what might happen," the PTC said.
"They chose a lineup full of performers who have based their careers on shock, profanity and titillation. Instead of preventing indecent material, they enabled it."
Madonna had promised that all efforts were being made to ensure her show would not be marked by a similar episode.
The halftime show has increasingly featured high-profile pop acts, a far cry from the first Super Bowl in 1967 when college marching bands entertained the crowd.
Paul McCartney, the Rolling Stones, U2, Prince, Bruce Springsteen, The Black Eyed Peas and Janet Jackson have been among recent performers.
