But Obama defended his record, rejecting what he said as Clinton's suggestion his supporters "were being duped" by him.
"Senator Clinton has a fine record. So do I," he said.
He also pointed to his opposition to the US invasion of Iraq, and Clinton's 2003 vote in favour of a senate resolution that authorised it, as an example of his judgment.
Obama said that on "the single most important foreign policy decision" of the decade, "I believe I showed the judgment of a commander in chief and I believe Senator Clinton was wrong in her judgment on that".
Clinton, who needs to win big victories in Texas and Ohio primaries on March 4, accused Obama of plagiarising part of a speech he had given.
"If your candidacy is going to be about words, then they should be your own words. That's, I think, a very simple proposition," she said.
"Lifting whole passages from someone else's speeches is not change you can believe in - it's change you can Xerox."
But Obama rejected accusations that he had stolen language from Deval Patrick, the Massachusetts governor who supports Obama, as "silly season" politics, and quipped: "I've got to admit, some of them [the speeches] are pretty good."
Cuba, where Fidel Castro, the ailing former leader stepped down this week, also featured prominently in the debate as the two candidates courted Hispanics who could play an influential role in the forthcoming Texas vote.
Obama expressed a willingness to move quickly towards a meeting with Raul Castro, the new Cuban leader, in line with his previous commitment to hold direct talks with leaders of hostile countries if he is elected president.
Clinton was more cautious, saying Cuba should first make progress on long-standing US complaints about the need to improve human rights and release political prisoners.
Obama pulled further ahead of Clinton on Thursday with the results of party polls for voters living outside the country, his 11th straight victory over Clinton.
The Democrats Abroad organisation said that Obama won about 65 per cent of the vote in countries and territories around the world, with Clinton winning 32.7 per cent.
The global primary results were cast between February 5 and February 12, with voters taking part at centres in more than 30 countries, by mail and fax and also for the first time via an online voting system.
Online votes were cast from 164 countries, the organisation said, including Antarctica, where a researcher at the US scientific mission at McMurdo cast his vote.
"With the US image so badly damaged by the present administration, American Democrats living overseas were eager to have their voices heard," Christine Schon Marques, international chair of Democrats Abroad in Geneva said in a statement.
"Across the board we saw an enormous diversity in participation, including many first-time voters."
Obama won 2.5 delegate votes while Clinton won two delegate votes.
An additional 2.5 delegate votes will be determined at the Democrats Abroad Global Convention in April.
Democrats Abroad also holds four superdelegate votes.