"There's no question that it's going to be hard," Kashkari said Wednesday at a news conference in the Orange County coastal community of Corona del Mar.
He had about 19 percent of the vote Tuesday compared with 55 percent for Brown, who also has more than $21 million in his campaign account and a lifetime of experience campaigning in California. Brown spent virtually no money and did not campaign in the primary.
Kashkari is a first-time candidate who is best known for leading the federal bank bailout at the height of the recession. He said his campaign will focus "like a laser" on issues such as job creation, improving schools and scrapping plans for the state's $68 billion high-speed rail line, a project that has been a priority of Brown's.
The 40-year-old former Goldman Sachs banker poured $2 million of his own money into his campaign, about 40 percent of his stated net worth.
The race between Kashkari and his GOP rival, state Assemblyman Tim Donnelly of the San Bernardino County mountain community of Twin Peaks, became a proxy fight for the future of California's Republican Party in a state that leans overwhelmingly Democratic. Donnelly, a tea party favorite who had worried some in the GOP establishment, conceded the race early Wednesday.
Brown returned to the governor's office in 2011 after serving from 1975 to 1983, in an era before voters enacted term limits. He told reporters Tuesday night that he takes nothing for granted in November, but he believes voters support his restrained approach.
"Someone once told me you win elections in the year before," he told reporters outside the historic governor's mansion in Sacramento. "What's won this election tonight is curing a $27 billion deficit, keeping my promise not to raise taxes unless the people themselves voted for it and bringing government closer to its people."
Meanwhile, Donnelly and Kashkari offered competing GOP visions. Donnelly, a social conservative who supports expanding gun rights and restricting immigration, concerned some of the Republican establishment with his heated rhetoric. Kashkari, an Ohio native, is the son of Indian immigrants who is a social libertarian and fiscal conservative. He pitched himself as the best person to restore the fortunes of the struggling party in California.
Republicans account for just 28 percent of the state's electorate.
The governor's race was the most high profile in Tuesday's primary, which also set the stage for several fiercely contested congressional races in the fall.