Longest-serving GOP senator loses primary fight NEW: Lugar concedes race to Mourdock Romney projected to win Indiana's GOP presidential primary Lugar is the Senate's longest-serving Republican and a foreign policy expert The Senate fight pitted moderate Republicans against the more conservative wing of the party Indianapolis (CNN) -- The Senate's longest-serving Republican became the latest casualty of the struggle between the GOP's conservatives and moderates as a tea party-backed challenger beat Indiana Sen. Dick Lugar in Tuesday's primary. Lugar conceded the race about an hour after the polls closed Tuesday evening, telling supporters that he congratulated State Treasurer Richard Mourdock on "a hard-fought race." Mourdock will face Democrat Joe Donnelly in November in a contest the nonpartisan Cook Political Report calls safely Republican. I want to see a Republican in the White House. I want to see my friend Mitch McConnell have a Republican majority in the Senate," Lugar said. I hope that Richard Mourdock prevails in November so he can contribute to that Republican majority. Lugar was first elected in 1976 and had sought a seventh term. But with more than 85,000 votes counted statewide, Mourdock was leading Lugar 64%-36%, state election returns show. Meanwhile, CNN also projects former Massachusetts Gov. Mitt Romney, the party's presumptive nominee, will win the Indiana's Republican presidential primary. All but one of Romney's rivals, Texas Rep. Ron Paul, have dropped out of the race. The 80-year-old Lugar is the former chairman and current ranking Republican on the Senate Foreign Relations Committee and is widely regarded as a leading voice on international affairs, particularly on nuclear proliferation. But he drew the ire of the tea party and other conservatives who criticized him as a lukewarm conservative, for voting for the 2008 bank bailout and for supporting President Barack Obama's Supreme Court nominees. That record drew him into one of the nastiest and most expensive congressional races in the nation -- one Democrats gleefully called a "tea party war." Tea party activists and other conservatives threw their support behind Mourdock, who led Lugar by 10 percentage points in pre-election polling. Lugar's campaign accused Mourdock of running a highly negative campaign funded primarily by special interest groups outside the state and of "bullying" Indiana voters. Mourdock's campaign painted Lugar as as an unreliable conservative and highlighted the fact that Lugar has not lived in Indiana since 1977. As voters trooped to the polls, Lugar told CNN that he was one of the bright spots in a body many see dimly. "The public as a whole may be unhappy with one party or the other, but they're very unhappy with the Congress as a whole for their inability to make decisions," Lugar said. I'm a person who makes sure we do get on with it, that there is progress, and with personal vigor I argue with people. "I try to persuade people, I try to get votes on issues, and I hope to continue to do that," he said. On Friday, Lugar called his opponent "unqualified to handle the complex situations in our world today." He warned the state's GOP voters, "Do not elect an unqualified person to serve in the Senate if you anticipate that you're serious about jobs and the security of our country and, as a matter of fact, cutting spending and the budget." But in a final ad released Friday, Mourdock said Lugar "has spent thousands of dollars telling you things about me that he knows are not true." Lugar told CNN on Tuesday he knew "that we had a campaign from the beginning," but believed his conservative credentials were strong. "Whenever the president has called for me to come to the White House for consultation, either by myself or with others, I have come," Lugar said. He has not frequently taken my advice, but I give it as an American. I think it's very important that the president hear the point of view of foreign policy that I've studied, and believe it's very important. But he noted that he had 100% ratings from the U.S. Chamber of Commerce, the National Association of Manufacturers and the National Federation of Independent Businesses. The fight pitted moderate Republicans against the more conservative wing of the party. Arizona Sen. John McCain, the party's last presidential nominee, endorsed Lugar, while McCain running mate Sarah Palin came out for Mourdock. The Democratic Senatorial Campaign Committee billed the contest a "tea party war" and decried what it called "the cannibalization of Dick Lugar" in a statement issued Monday. Super PACS spent $4.6 million to exacerbate the fight, with outside groups spending nearly $3 million to support Mourdock. CNN's Dana Bash and Shannon Travis contributed to this report.