The government has handled the events surrounding the Iranian capture of navy personnel "shambolically", the Conservatives have said.
Two of the crew have been paid for their stories
Leader David Cameron described the decision to allow the freed crew to sell their stories as "calamitous".
Although Defence Secretary Des Browne has accepted final responsibility for the controversial decision, Mr Cameron said further explanation was needed.
He said it was such a serious issue that a full MoD inquiry was needed.
Mr Browne gave his first interview on Wednesday, after increasing criticism about the navy's decision to allow two of the 15 sailors and marines to sell their stories to the media following their release last week.
Iran captured the 14 men and one woman on 23 March after saying they had strayed into their territorial waters. Britain maintains that the crew were in Iraqi waters under a UN mandate.
Following the backlash about them being paid for their stories, further sales have been banned.
Mr Browne said he had accepted the navy's decision to allow the personnel to tell and sell their stories but that, with hindsight, he could have handled things differently.
But Mr Cameron said: "The events surrounding the taking of our armed service personnel hostage in Iran have been handled shambolically."
Mr Cameron said although Mr Browne had finally spoken out about the decision, questions remained unanswered about "this... dreadful decision".
"We need to know when did he consult with Downing Street, what did Downing Street say, what was the involvement of the prime minister?
"Those are the questions that now need to be answered, but we've also got to learn the broader lessons.
"What is it that went wrong, why was this allowed to happen and can we have a proper, full Ministry of Defence inquiry that then is made public, and reported to Parliament, that should be equivalent to a board of inquiry," Mr Cameron said.
He said the government "gives every impression of just being cheap and tatty, that they put tomorrow's headlines ahead of concerns about the long-term damage that they might do".
"They've done long-term damage to Parliament, they've done long-term damage to the civil service and its independence and now, I fear, they are doing long-term damage to our Armed Forces," he added.
"We mustn't let that happen, we need a proper explanation," he said.
"We haven't had that yet from the prime minister and in the end the buck stops with him".
Mr Browne had earlier admitted that "ultimately, the buck stops here" when questioned about the decision.
Mr Browne told the BBC he had been asked on Friday "to note" the navy's decision to allow the freed personnel to sell their stories.
He said he, and the navy, were "not content" with the decision but felt they had little choice, given that the stories had to be told in the freed captives' own interests "to counteract the propaganda the Iranians had put out using them".
The view the navy took, following "analysis of regulations", was that given the stories would have to be told, the people concerned could not be prevented from being paid.
But, he added, after further discussions with officials on Monday his view of whether the selling of stories could be banned changed, he said.