Pol Gen Adul said police were unable to fully protect the People's Democratic Reform Committee (PDRC) march because it altered its route so abruptly.
He denied police links to the bomb, which exploded near to where PDRC leader Suthep Thaugsuban was leading protesters in a march to drum up support for the anti-government group.
Caretaker Prime Minister Yingluck Shinawatra has assigned him to investigate the explosion, the national police chief added.
The PDRC had planned to walk a different route from their Lumpini Park rally stage, but demonstrators changed course and marched to Banthat Thong instead, Metropolitan Police Bureau deputy commander Adul Narongsak said.
Pol Maj Gen Adul Narongsak questioned why the march route had been changed but did not indicate how or if the new route was connected to the bomb attack.
He called on protesters to allow police forensic experts to go into the rally area to collect evidence. Protesters have refused police entry to a nearby building believed to be the place where a suspect threw the bomb at demonstrators for fear they could tamper with evidence.
PDRC guards have so far only allowed soldiers to enter the building thought to have been the hiding place of the suspect.
The bomb used in the attack is believed to have been an M26 grenade, a grenade cap for which was found at the blast site.