Johnson told Entertainment Weekly that the new sci-fi drama compares favourably to the likes of ABC's Lost and fellow Fox series Fringe.
"This show will be easier to tune in to every week than a Fringe or a Lost," she said. "Really at the heart of Alcatraz is [the concept of] pursuing the inmates.
"Every week we'll be catching or not catching one of those inmates. The mythology will be there if you're looking for it, but it won't be critical to enjoying each episode."
Johnson also discussed the show's recent reshoots, insisting that the new material filmed for early episodes will "strengthen... the dynamics of the [central] group, and the crime of the week".
"We had already hit the sweet-spot in the flashbacks and the stories we were telling at Alcatraz," she said. "[But] we felt that there was room for understanding the characters better.
"[The reshoots helped with] understanding Rebecca's backstory, and why she was invested in the task force, understanding her relationship to Soto, and strengthening those relationships. And then also [we wanted] the hunting of the fugitive of the week to be as mesmerising and exciting as it could be."
The Alcatraz double-bill premiere was a ratings hit for Fox on Monday night, pulling in a peak of 9.97m viewers.
The series continues on Mondays at 9/8c on Fox.
> Alcatraz: 'Pilot' recap
> Alcatraz: 'Ernest Cobb' recap
Watch a behind-the-scenes Alcatraz video featurette below: