The criticism came from lawyers acting for the Arkinson family.
Arlene, 15, from Castlederg, went missing in August 1994.
Her body has never been found. Robert Howard, who died in prison last year, was the main suspect.
A retired police officer defended the handling of the case but said he was unable to provide an explanation for the delay in arresting Howard.
"I unfortunately am not in a position to give a reason why there was such a delay," said Neil Graham, a former detective inspector.
"I would love to give a reason."
Mr Graham added that all elements in a high-profile case would have been considered by a senior team.
He said that despite a significant number of searches, including a search of Howard's flat, there has never been any forensic evidence found.
"The concept of police pursuing a successful criminal investigation in the absence of evidence or a body had not been tested in any form," he said.
"I have no doubt that the senior investigating officer would have been very mindful of those facts, particularly in consultation with the prosecution service."
The inquest also heard from a detective constable who arrested Howard in 2004 on suspicion of the murder.
He said that he had a conversation with Howard in which the suspect "opened up to him".
He recalled Howard asking: "Assuming that I could help, where would I serve my time?"
The witness said that the matter was not pursued by him or, he believed, by a senior officer he had given the information to.
The police investigation into the disappearance of County Tyrone teenager Arlene Arkinson was a case of the "left hand not knowing what the right was doing", an inquest into her death has heard.