The officers are angry that they received no orders on how to deal with anti-government protesters at the Thai-Japanese sports complex in Din Daeng district.
National Police Chief Adul Saengsingkaew and his deputy, Pol Gen Worapong Chiwpreecha, are among the targets of the complaints.
The officers began venting their frustration after the death of a colleague who was shot during the confrontation with protesters on Thursday, a police source said on Friday.
Pol Sr Sgt Maj Narong Pitisit, 45, succumbed to his injuries after he was shot in the chest by an unidentified gunman at the venue on Thursday.
One policeman wrote on LINE that the officers tasked with handling demonstrators both inside and outside Bangkok were losing morale because the protesters are armed with guns.
"Officers had no intention to move in on the protesters," he wrote. "We didn't know how to act because we didn't receive any orders from our commanders. We were like sitting ducks out there."
According to the source, many lower-ranking police officers are considering bringing their pistols for protection as they perform their duties. Some may start to disobey orders to confront the demonstrators if the lack of command continues.
Officers also shared on LINE pictures of official documents addressed to their superiors, asking them to find solutions to ensure the safety of those keeping order at protest sites.
The request was signed by Pol Sub Lt Thanakorn Huaykuadwattana, an inspector at Don Tum police station in Nakhon Pathom.
The Royal Thai Police have acknowledged the complaints that have been circulating and are trying to resolve the problems, the source said.