The show was produced by Star Trek director JJ Abrams, and has a 63 per cent approval rating on review aggregate site Metacritic.
"For now, Alcatraz is a sinister bag of sinister pleasures," said Miami Herald's Glenn Garvin after the show's first episode.
Fans had mixed feelings about its cancellation.
"My constant need for answers led me to getting fairly frustrated with this show so it's cancellation comes as no surprise. Plus at no point did Sam Neill fight a dinosaur. Trick missed there," said one posting online.
"A show with amazing potential, sadly let down by extremely poor characterization. It's incessant need to keep everything a mystery meant we couldn't get to know the charters at all," said another.
Alcatraz is due to air on TV One later this year.
Watch the trailer for Alcatraz:
- Herald online