Kofi Annan was speaking two days after a bomb devastated the UN's Baghdad headquarters, killing 20 and injuring more than 100.
Although Annan refused to blame the United States for the disaster, he emphasized America was responsible for security around the UN headquarters.
"We had hoped that by now the coalition forces would have secured the environment for us to be able to carry on... economic reconstruction and institution building... That has not happened," he said.
"When you take on such a complex operation, one has to do planning ahead and I think there have been some wrong assumptions all along.
"The coalition has made some mistakes and maybe we have made some mistakes too," he added.
However, the blast has cast doubt over the UN's future role in Iraq.
UN spokesman Fred Eckhard said Annan had to assess whether "we are going full speed ahead or scaling back a bit".
At the moment, UN Baghdad staff are being evacuated while an alternative headquarters is being contemplated.
Colin Powell will meet with Annan
to discuss the UN's role in Iraq
The United Nations has already suspended operations and has told anyone who wants to leave they can do so.
Many others have been urged to leave Iraq for a rest "just so they can calm themselves down and better prepare themselves to resume their task", Eckhard said.
Meanwhile, Annan is due to meet US Secretary of State Colin Powell and British Foreign Secretary Jack Straw on Thursday.
Both officials have proposals for another UN resolution to encourage nations to send troops and police for security in Iraq.
The United States is unlikely to cede any control in Iraq to the United Nations or other nations, although Britain is considering it.
One State Department official said Washington might be prepared to expand the UN's role, but only if the Security Council gave guarantees the United States would retain ultimate control.
"A lot of things are being looked at with respect to mandates," an official said.
"But whether we can work something out that satisfies everyone is up in the air."