DETROIT — The U.S. government ended up losing $10.5 billion on the General Motors bailout, but it says the alternative would have been far worse.

The Treasury Department sold its final shares of the Detroit auto giant on Monday, recovering $39 billion of the $49.5 billion it spent to save the dying automaker at the height of the financial crisis five years ago.

Without the bailout, the country would have lost more than 1 million jobs, and the economy could have slipped from recession into a depression, Treasury Secretary Jacob Lew said.

Now, the American auto industry is back, President Barack Obama said. “Some of the most high-tech, fuel-efficient cars in the world are once again designed, engineered, and built right here in America — and the rest of the world is buying more of them than ever before,” he said.

The government received 912 million GM shares, or a 60.8 percent stake, in exchange for the bailout in 2008 and 2009. It began selling shares once GM went public again in November of 2010, and the pace picked up this year as the stock rose more than 40 percent.

The auto bailout was part of the Troubled Asset Relief Program, with the bulk of the money going to financial institutions. Treasury said it spent $421.8 billion on bailouts and so far has recovered $432.7 billion, including the loss on GM.