Instead of ordering more episodes, which would be a sure sign that NBC is happy with the show, Constantine will only have 13 episodes in its first season. On the other hand, the numbers have been improving, so it could still pull off a renewal.
Before the show even premiered, NBC showed confidence in it by ordering three extra scripts for the show. And now, according to Deadline, those scripts (one of which would have introduced Dr. Terrence Thirteen) won't be produced this season. Deadline also cautions against reading this as a cancellation, hearing that the show remains "in contention for a second-season renewal."
Basically, because Constantine premiered later in the year than other shows, NBC has less information about its ratings than it does other shows. And Constantine hasn't been a huge ratings success right out of the gate, which would make the decision easy. So, says Deadline, NBC's splitting the difference: Not spending money on new episodes now, but leaving open the option for renewal if the ratings continue to pick up for the remaining eight episodes. (Which it did for episode 4.)
There's also the chance that NBC just refuses to let go of its sole comic-based property, with that particular branding is so hot in Hollywood right now, and given that both Gotham and The Flash are making full seasons of episodes, the failure of Constantine may look like a failure on NBC's part to pick the right project and/or make it properly. All of this leads me to believe the Deadline report that the show is on the very tip of the bubble, rather than cancelled in everything but name.