Many UK officials have been critical of US policy after the war
Mistakes made before and after the US-led invasion of Iraq in 2003 must not happen again, a top diplomat has said.
Sir Jeremy Greenstock, the former UK ambassador to the UN, said the entire mission had been "rushed" and had not had enough international input.
He told the Chilcot inquiry the UK had been a "minor partner" and had not had enough clout to affect key decisions.
The broadcast of Tuesday's hearing was cut off for more than a minute by its chairman on national security grounds.
Sir John Chilcot said he had interrupted the TV coverage because "sensitive information" was being discussed.
Asked about the lessons from the UK's involvement in the invasion and its aftermath, Sir Jeremy said post-war planning must be regarded as just as important as the military campaign while security had to be prioritised if anything else was to be achieved.
"This was clearly too rushed an exercise for the size of the task we found on the ground, a task which some people had been predicting would be as difficult as it was," he said.
AT THE INQUIRY
BBC World Affairs correspondent Peter Biles
As a career diplomat, Sir Jeremy Greenstock chooses his words with the utmost care.
So it was a surprise when his evidence was interrupted for reasons of "national security". Proceedings were halted as Sir Jeremy was explaining that his assessment of the American view of Iraq in 2003/4 was gloomier than the prognosis which US Administrator Paul Bremer was reporting to The Pentagon at the time.
The words "Public Hearing Temporarily Suspended" flashed up on the video screen in the media centre as the inquiry chairman, Sir John Chilcot, took advantage of the one minute broadcast delay for the first time.
Were these "exceptional circumstances", with Sir Jeremy Greenstock on the point of causing harm to national security ? At this stage, we do not know. The transcript of this key moment of the hearing will simply contain a line of asterisks when it is published on the Inquiry's official web site.
"To have this degree of mismatch is something which has to be avoided in the future."
There had not been sufficient "international input" into the post-war administration of Iraq, he said, eroding support for the mission.
UN officials had envisaged playing a "leading role" in political reconciliation and institution building in Iraq, a view shared by UK ministers.
But it became clear in the weeks after the invasion that the US planned to be "in sole control".
"We were conscious that the US was going to place a very definite limit on the degree of responsibility that it would allow anyone other than the US in dealing with Iraq after the conflict," he said.
Former Prime Minister Tony Blair urged President George W. Bush to give the UN a "vital" role in Iraq so it was not seen as subordinate to the US, Sir Jeremy added.
But he said Washington viewed the UN's remit as being restricted to practical matters, such as guaranteeing supplies of food and medicine, and not as an equal partner.
Sir Jeremy left the UN to work for the US-led Coalition Provisional Authority (CPA) which ran Iraq from May 2003 until June 2004.
The CPA was supposed to stabilise Iraq, promote reconstruction and pave the way for democratic institutions but was heavily criticised for many of its decisions as violence escalated over the period.
November-December: Former top civil servants, spy chiefs, diplomats and military commanders to give evidence
January-February 2010: Tony Blair, Gordon Brown and other politicians expected to appear before the panel
March 2010: Inquiry expected to adjourn ahead of the general election campaign
July-August 2010: Inquiry expected to resume
Report set to be published in late 2010 or early 2011
Sir Jeremy told the inquiry that Paul Bremer, the head of the CPA, had not wanted him as his formal deputy, as opposed to the UK's chief representative on the body, in order to keep US control of the operation.
While maintaining "an independent voice" for British interests, he said he was not able to exert influence over key decisions outside the UK's direct area of operation in the south of the country.
"We were uncomfortable about the low-level of planning for post-conflict Iraq, had worries about under-resourcing, and were never able to persuade the Americans why we thought it should be done differently.
"In that very major respect, our influence was too low."
He blamed this on a lack of UK troops and resources on the ground.
"Money means influence...with the Americans as much as argument or position of first ally." he said.
In its first month, the inquiry has heard from senior civil servants, diplomats and military commanders about the origins of the invasion, Iraq's military threat and post-war contingency planning.
In an earlier appearance, Sir Jeremy said he believed the invasion was of "questionable legitimacy" as most UN members did not support it.
Senior politicians, including Tony Blair, are to appear before the inquiry next year, with its report due to be published in late 2010 or early 2011.