I thought the Patriots got an extra time out too when watching the game, but I watched on tivo and realized the problem was that Fox inaccurately took away a timeout thinking the Patriots had called one earlier in the fourth quarter when they didn't. The clock didn't stop. It took a while for them to figure out the mistake, but they got it correct.
As for the other team complaining after a tough loss, we do it too. Has anyone read the Cinci post-game thread? We're no different than they. Sure, every once in a while someone posts something like "I thought the Patriots got away with ____" and then declares themself the one true objective fan in the universe. But everyone watches a game through their own prism.
Interestingly, though, nobody is being unfair or "biased" in a pejorative sense. Perception is an extremely complicated phenomenon. It's more complicated than a pithy statement, but there is a great deal of truth to the axiom that one sees what one wants to see. But the point is that Saints fan truly do see the game different from how we do -- that is, they actually perceive it differently. Of all the information provided to their brains, their brains process and assimilated differently from how our brains see the exact same event. It's the nature of the business. Lots of great experiments about this. None more seminal and groundbreaking than the original word on the subject -- a 1954 scholarly journal about a game played in 1951 -- "They Played a Game." As the authors conclude, while one game was played, the only thing that ultimate matters is how the game was experienced by each of its viewers or even by those who didn't view it but heard about it and viewed it later. It's not just "a" game, but millions of games, every single one of them different.
Selective Perception: They Saw A Game by Albert H. Hastorf & Hadley Cantril