Santorum Says, "On to South Carolina"; Campaign "Loaded for Bear" T.J. Kirkpatrick/Getty Images MANCHESTER, N.H. - Rick Santorum had a disappointing showing in the New Hampshire primary tonight, battling with Newt Gingrich for fourth place, and just cracking double digits late Tuesday evening. Despite the result, Santorum, standing next to his wife Karen, told supporters he would keep fighting. "On to South Carolina," he said to the small group - an equal number of journalists and supporters - gathered at a restaurant here. Late tonight they planned to head to the Palmetto State, where they will try to engage with an electorate that is more aligned with his socially conservative policy stances to regain the momentum he grabbed with his virtual tie with Mitt Romney in Iowa last week. Santorum's national communications director, Hogan Gidley said they would dump much of the $3 million they have earned since Iowa into the Palmetto State. "We are loaded for bear," Gidley said after Santorum's speech. Santorum said he wanted to "respect the process" by coming to New Hampshire and competing here, adding they wanted to "respect the fact that we are going to campaign in every single state, states that were good for us and states that may be a little tougher." He also gave Romney, the New Hampshire victor, a gracious congratulation, saying the campaign front-runner "fought hard in this state." "For those who would like to say this would be over in one or two states that have been, well, let's say the backyard and the home of a certain candidate, which by the way I want to absolutely congratulate Mitt Romney on a great victory tonight," Santorum said. (I'm) looking forward to engaging on the subject of issues, talking about records, how we are we going to put the best foot forward, the best person forward. Santorum added to cheers: "We can win this race." At his party at the Derryfield Restaurant, a much smaller group of supporters than attended his event in Iowa or even any of his New Hampshire stops waited for the candidate to speak. A group of about one-sixth the size of the throng that greeted him last week in the Hawkeye State stood around politely and mingled listening to music like Bette Midler's "Wind Beneath My Wings." State representative and New Hampshire co-chair Daniel Tamburello said Santorum would show he's the "true conservative alternative to Willard Mitt Romney" in the Palmetto State. Santorum walked off the stage to The Beatles, "It's a Hard Day's Night." It was a stunning contrast from a week ago, when he was swarmed by supporters and press and defiantly told the crowd, "Game on!" Although it was no surprise he didn't do well in libertarian leaning New Hampshire, unlike Rick Perry, Santorum did compete here. He made 32 trips to the Granite State over the last year, second only to Jon Huntsman. His campaign manager is a New Hampshire native and the candidate was coming into the state with the Iowa momentum at his back. Even tonight he mentioned the social conservative foundation of his campaign, promising supporters he would be "the conservative that understands the foundation of our country, the institutions that are crucial for us to be a successful nation: families, families that are bonded together are the foundation ... to build a great nation from the bottom up, that's the message." The campaign is stressing their "good operation" in South Carolina, adding they have "lots to look forward to" in the Palmetto State. The campaign says they "knew they would always be neck and neck with Gingrich here," but they point out they didn't have money to go on the air, only running one television ad on cable in the state, and they did not have the endorsement of the state's largest newspaper, the Union Leader, which Gingrich did. Santorum was scheduled to travel to South Carolina tonight with none of the momentum that he sailed into this state with, and only 11 days to pull off victory. ABC News" Jake Tapper and Daniel Steinberger contributed reporting.