Lugar, 80, was ousted in the GOP primary by state Treasurer Richard Mourdock, who hammered him on his record of working with Democrats during his six-term career in the Senate.
Lugar said on CBS' "Face the Nation" that Mourdock's victory was the result of a major boost from out-of-state special interest groups who were more concerned with political power than with effective government.
"It happened in large part because we had a Republican primary," Lugar said. "A large portion of the Republican Party of Indiana believed apparently in the idea of individualism as opposed to community; a sense of compromise or a sense of talking across the aisle," Lugar said. "I think that's still true of a majority [of Indianans] has supported me in our efforts both in foreign policy, farm policy and other situations to forge things that worked, and so I intend to continue to do that."
Lugar said he suspected the reason Mourdock and his allies attacked him with such vigor was because it was the only shot they had to knock off an incumbent Republican senator this year.
He also said he hoped Indiana Republicans would get behind Mourdock. "I would say that I have offered advice to my former opponent and now candidate as to trying a way he could be a constructive senator," he said.