The Republican presidential hopeful told "Fox News Sunday" that the president is partly to blame for the chaos there and should have been "more engaged" with military commanders and Afghan President Hamid Karzai.
Romney has emerged as the only GOP candidate not to question the U.S. commitment in Afghanistan, even as polls show that most Americans want to end it.
Administration officials say leaving behind a stable Afghanistan has been a top priority for the president. Obama plans to pull troops out by the end of 2014.
Romney said any U.S. withdrawal should be determined by military commanders. At the same time, he said, Afghans should be taking more responsibility for security because "we're not going to stay there forever."