사항지지 않아 doesn't make any sense. 믿어지지 않아 means "I can't believe it". It is the same -지 않다 used on the verb 믿어지다. 믿어지다 = 믿다(believe) + 어 + 지다(become; settle into). 믿다 is "believe" in its active sense, while 믿어지다 is like a passive form, meaning something comes off as believable. So 믿지 않아 is "I don't believe it" whereas 믿어지지 않아 is "I can't believe it" or "It is not believable to me". - I don't believe that: 나는 그걸 믿지 않아. - I can't believe that: (나는) 그건 믿어지지 않아. (It is not believable) 느끼다 / 느껴지다 (=느끼어지다) is another example of such formation. 나는 날씨가 춥다고 느끼지 않았다 => I didn't feel it was cold. 나는 날씨가 춥게 느껴지지 않았다 => It didn't feel cold to me.