Zbigniew Brzezinski, who served under President Jimmy Carter from 1976 to 1980, also made a scathing assessment of the ensuing occupation after Saddam Hussein was ousted as Iraqi leader.
He said the US administration will now have to scale down its ambitions for Iraq's future.
"I personally think it was not worth it, in the sense that we have paid a high price in blood. And it's increasing. You cannot underestimate the suffering that this has already produced to tens of thousands of American families," he told CNN.
Brzezinski also said tens of thousands of Iraqis had died and that the US was spending billions of dollars and had isolated itself internationally.
"Now, that is simply not worth the price of removing Saddam,
because we were containing him. But we are where we are. And the problem today is, in my judgment, how to avoid failure."
Kissinger supports invasion
Brzezinski said the US "will confront a continuing problem and maybe a deepening crisis if there remains a massive disproportion between objectives, which are unrealistic, and means, which are very limited.
"If we are very serious about creating an Iraqi democracy, let us put in 500,000 troops and let us spend $100 billion, $200 billion. We are not going to do it and, therefore, we have to scale down our expectations."
"I personally think it was not worth it, in the sense that we have paid a high price in blood ... And the problem today is, in my judgment, how to avoid failure"
Zbigniew Brzezinski, former US national security adviser
On the other hand, former US secretary of state Henry Kissinger expressed support for the invasion on the same CNN programme.
Kissinger remains a strong supporter of the Bush administration line.
But he said the US administration had misjudged the difficulty of rebuilding Iraq and guiding it to democracy.
"I believe that they made fundamentally the right decision in
entering the war. But they underestimated the complexity of
rebuilding a democratic society in Iraq under military occupation," he said.
Kissinger said the whole administration leadership, and not just embattled Defence Secretary Donald Rumsfeld, had to look again at the political decisions made.
Henry Kissinger supports
the Bush administration line
The two former US officials also disagreed over the future makeup of Iraq's government.
Brzezinski said there was now a growing probability that a "Shia theocratic government which is not going to be a genuine democracy" would win Iraq's elections to be held on 30 January.
Kissinger said the US should not accept a Shia theocracy for all of Iraq.
"And if it reaches this point, then we really have no interest in keeping Iraq united.
"Then we might just as well let each of these competing ethnic groups create their own self-government, rather than imposing a theocracy on, or cooperate with creating a theocracy for, all of Iraq."