The AP often is the sole media presence at US executions, and explains the American death penalty process to the world.
Media witnesses hold government officials accountable when executions are flawed. In recent years, reporters have been able to witness and tell the public about botched or problematic executions in Alabama, Arizona, Oklahoma and Ohio, where inmates could be seen gasping for breath for long periods of time or writhing and clenching their teeth while on the gurney.
Reporters have also highlighted efforts by states to prevent the public from knowing the source of lethal injection drugs they use.
An investigation into what led to the miscommunication in Texas continued on Thursday (US time), said state Department of Criminal Justice spokesman Jeremy Desel. It was unknown how long the investigation would take to complete.
"We are taking steps to ensure that what happened doesn't happen again in the future," he said.
Desel said the prison agency does not believe any state laws were violated by not having media witness the execution. The Texas Code of Criminal Procedure does not specifically mention media in connection with witnessing an execution, Desel said.
A part of the Texas Administrative Code - rules and regulations that govern state agencies - lists individuals who are authorised to witness an execution, including a media pool consisting of five reporters.
The AP is specifically designated as one of the five pool reporters. Desel said the administrative code "does not mention or use the word must in any way, just that the following persons may be authorized to witness".
In a Thursday tweet, state Rep. Jeff Leach, R-Plano, welcomed the investigation.
"It was 'a mistake' and/or 'a miscommunication' is not acceptable. This is an unfathomable, colossal screw-up and we need answers," he said.
The office of Governor Greg Abbott did not immediately reply to an email seeking comment.
Robert Dunham, executive director of the Death Penalty Information Centre, said while the administrative code is written in a way to give the state has some deniability as to whether it violated the law, not letting reporters witness Wednesday's execution was a violation of the law and "describing it as anything but that is parsing words".
The mistakes that led to what happened on Wednesday speak to the ability of Texas and the 23 other states that currently have the death penalty to carry out executions, said Dunham, whose group takes no position on capital punishment but has criticised the way states carry out executions.
"Texas has more experience in carrying out executions than any other jurisdiction in the Western Hemisphere and if Texas can make a mistake like this, what confidence can the public have in what other states are doing?" he said.
Joseph Larsen, a Houston attorney who is also on the board of directors of the Freedom of Information Foundation of Texas, called the lack of media witnesses "inexcusable" and executions "must be done with complete transparency to maintain the integrity of the judicial process".
"It is not different from requiring that the trial of the person charged be public and witnessed," he said. "Texas officials would like to restrict media access to the extent (most) possible, mostly for political reasons."
Larsen also believes the Texas Department of Criminal Justice violated state law by not having media witnesses on Wednesday. Executions were once held in front of courthouses and often turned into public spectacles but since they became "more solemn and sombre activities" within prison walls, the media has functioned as a way "to ensure public accountability and to report if anything goes wrong," Dunham said.
No reporters during Wednesday's execution also meant the public wasn't able to get firsthand details from the media about several changes that have been made in the execution procedure.
Accommodations have been made to allow an inmate's spiritual adviser in the death chamber.
Last month, prison officials reversed a two-year ban on advisers created after the US Supreme Court halted the execution of an inmate who had argued his religious freedom was being violated because his Buddhist spiritual adviser wasn't allowed to accompany him.
The death chamber has also undergone some renovations, including soundproofing and new paint and carpet.
Dunham said states and the media have an uneasy relationship when it comes to executions as states need the media to preserve the legitimacy of executions while they try to also avoid accountability when things go wrong.
"It's a balance between legitimacy and accountability," he said. "States need the media, but they also want to restrict it."