Somyot Pumpanmuang said the officers deserved it as there had been no public tip-off to help them.
The 17 August blast, which the government called the worst such attack in Thailand, killed 20 people.
One man has been arrested, and warrants have been issued for two other people.
It is not clear if the unnamed man detained by the police is the chief suspect in the attack. Police have said they do not believe he is the man seen in CCTV footage at the shrine just before the explosion.
Police say the suspect under arrest is a 28-year-old foreigner and that bomb materials were found at his home.