Jets kicker Nick Folk missed a 56-yard field goal attempt but was handed a reprieve when defensive lineman Chris Jones was penalised for pushing a teammate from the second line of defence - the first time such a penalty has ever been called in the NFL.
Folk went on to score another effort from 42 yards to seal the win and Jones took full responsibility for the penalty after the match.
However, Belichick insists that it was his fault as Jones was acting under orders and also admits that he was wrong when he claimed it was not a penalty in his post-match comments.
"On the field goal play at the end, Chris is obviously trying to do the right thing by stepping up and taking responsibility. But that's not his responsibility. That's ours. I just have to do a better job of coaching that. That's not his fault," ESPN quotes Belichick as saying.
"Obviously we are wrong. It's our job to understand the rules. Whatever the bottom line is, we didn't do it properly. We've got to coach it better. What he did was basically what he was being told to do."
Despite the defeat, the Patriots remain top of the AFC East with a 5-2 record.