Mr Obama made the admission in interviews with US TV networks during his tour of Asia.
He said he was "not disappointed" that the deadline had slipped, saying he "knew this was going to be hard".
Officials are trying to determine what to do with some 215 detainees still held at the US prison in Cuba.
Mr Obama's announcement follows considerable speculation that the deadline would slip, as the administration wrestles with how to deal with those inmates who cannot either be freed or tried in US courts.
He did not set a specific new deadline for closing the camp, but said it would probably be later in 2010.
"We had a specific deadline that was missed," he told NBC.
And he told Fox News: "It's hard not only because of the politics. People, I think understandably, are fearful after a lot of years where they were told that Guantanamo was critical to keep terrorists out."
Closing the facility was "also just technically hard", he added, and depended on co-operation from Congress.
Moving to close Guantanamo was one of Mr Obama's first acts in office.
BBC News website world affairs correspondent
President Obama's admission that he will not close Guantanamo Bay by his target of 22 January is not a surprise given that his senior officials have been hinting at this for some time.
The problems have proved more complex than expected. Most difficult of all is what to do with those prisoners against whom there is not enough presentable evidence to use either in a civilian or a military court. The US government is trying to get foreign countries to take them but has had limited success.
There is some domestic opposition to their transfer to the US itself. A nearly-empty prison in rural Illinois is being considered to house them. The president's statement is an acceptance that this will not be resolved in time.
On 22 January 2009, just two days after inauguration, he set a deadline of a year for closing the heavily-criticised prison.
His administration says it will try some detainees in US courts and repatriate or resettle others not perceived as a threat.
Last week, Attorney General Eric Holder announced the alleged mastermind of the 9/11 attacks, Khalid Sheikh Mohammed, and four other defendants would be transferred from Guantanamo to face trial in a New York federal court.
Some lawmakers and relatives of 9/11 victims reacted angrily, arguing that the move put Americans at risk.
Asked about domestic opposition, Mr Obama told NBC that the anger over Khalid Sheikh Mohammed's civilian trial would disappear "when he's convicted and when the death penalty is applied to him".
And in separate comments to CNN, he said that the notion that "terrorists possess some special powers that prevent us from presenting evidence against them, locking them up and exacting swift justice" was a "fundamental mistake".
In terms of other detainees, five have been ordered to face military commission trials in the US and a number of others, including several Chinese Muslim Uighurs, have been cleared by investigators for release and resettled overseas.
But the issue of detainees assessed as dangerous but who for legal reasons could not be successfully prosecuted in US courts remains unresolved.
The BBC's Jonathan Beale, who is at Guantanamo Bay, says the announcement of the delay to the deadline has come as no surprise.
The question of where to put those detainees who cannot be freed or tried remains a huge political obstacle, he says.