The U.S. is safer and better informed about Russian election interference because of special counsel Robert Mueller’s investigation, Deputy Attorney General Rod Rosenstein said Thursday night in a fiery speech in which he lashed out at critics and defended the decisions that defined his time in office.

In his first public remarks since the release of Mr. Mueller’s report, Mr. Rosenstein criticized the Obama administration as being slow to publicly address Russia’s efforts to undermine U.S. elections and slammed former FBI...