By JANET HOOK and NEIL KING JR.

Mitt Romney sought to shake off his bruising losses in three battleground states as his campaign promised Wednesday to spend heavily on coming contests to regain his position as the front-runner for the Republican presidential nomination.

But the defeats suffered by the former Massachusetts governor in Tuesday's primary and caucuses in Colorado, Minnesota and Missouri exposed lingering weaknesses in Mr. Romney's standing with conservatives.

The losses to a newly resurgent Rick Santorum, the former Pennsylvania senator, also showed a lack of enthusiasm for Mr. Romney in states where his campaign declined to spend significant time and money.

Although the contests didn't directly award GOP delegates, the voting patterns revealed warning signs for Mr. Romney, who has won just three of the eight GOP contests so far: New Hampshire, Florida and Nevada.

In Missouri, Mr. Romney failed to win a single county in a state seen as a crucial battleground in the November general election. The Romney campaign dismissed the outcome because turnout was small. But the 250,000 voters who cast ballots Tuesday amounted to nearly twice the number that voted the Iowa caucuses earlier this year.

Mr. Romney also didn't win any counties in Minnesota, a state where the Republican Party is dominated by religious conservatives who were attracted to Mr. Santorum's campaign.

In Colorado, Mr. Romney won just 16 of the state's 64 counties. Mirroring patterns of support in other states so far, he fared best in more-affluent communities. He won in Denver and surrounding suburban counties, but that support failed to overcome Mr. Santorum's tallies in the rest of the state.

Two of Mr. Santorum's upsets came in states that Mr. Romney won four years ago, Colorado and Minnesota. In both, despite a superior campaign organization, Mr. Romney's vote tallies shrank from his 2008 totals.

"We didn't devote a lot of money and time to the states yesterday," Mr. Romney said Wednesday in Atlanta, seeking to play down his losses. "We were spending our time and money in Florida and Nevada."

He then took jabs at both Mr. Santorum and former House Speaker Newt Gingrich, who was positioned until just days ago as Mr. Romney's top rival.

An emboldened Mr. Santorum boasted Wednesday that his campaign took in $250,000 overnight. He campaigned Wednesday in Texas, which holds its election in early April, and was headed to Oklahoma on Thursday.

Mr. Santorum's campaign plans to make a serious push in Michigan, Mr. Romney's home state. "We're trying to show that we're the alternative to Mitt Romney in every state, and Michigan is no different," said Santorum campaign spokesman Hogan Gidley.

Mr. Santorum has won four contests—in Iowa on Jan. 3 and the three states that voted Tuesday. Mr. Gingrich scored his lone upset win in South Carolina last month.

Mr. Romney's team plans to paint Mr. Santorum as a Washington insider with a penchant for costly public spending projects. Mr. Romney gave a preview Wednesday. "I think a lot of us feel that the Republican party lost its way in the past," he said. "Republicans spent too much money, borrowed too much money, earmarked too much, and Rick Santorum and Newt Gingrich have to be held accountable."

Mr. Romney's campaign promised to spend big in coming weeks, with an eye toward contests in Arizona and Michigan on Feb. 28, and the March 6 Super Tuesday that spans 10 states.

Tuesday's vote was the latest turn in a careening GOP nominating contest, with Mr. Santorum's victory a blunt reminder of Mr. Romney's uncertain hold on his party's base.

"If I were in Boston today, I would be very concerned," said Ed Rollins, who has advised numerous Republican presidential campaigns. "The reality is that conservatives want an alternative, and Romney just isn't making the sale."

Arizona Sen. John McCain, who lost 20 state contests on the way to the GOP nomination in 2008, disagreed. "I don't think it's a problem for Romney," he said.

Mr. Gingrich, who posted poor showings Tuesday in Colorado and Minnesota, is betting on a strong performance in Southern states that vote on Super Tuesday. He campaigned Wednesday in Ohio, one of the March 6 primary states.

Mr. Gingrich toured a Cleveland manufacturing plant and talked about the economy, but he didn't discuss Tuesday's losses. Campaign spokesman R.C. Hammond said the outcomes were "a demonstration of how weak Romney is among conservatives in the party."

An independent group supporting Mr. Romney, Restore Our Future, went on the air Wednesday in Ohio with a campaign ad saying Mr. Gingrich carries "tons of baggage" and Republicans risk losing the election if he is nominated.

All the candidates will now be out raising money, with Mr. Romney holding the advantage. His campaign had some $19 million at the end of 2011, and though it has spent heavily on ads since, it is expected to have much more cash on hand than rivals.

Mr. Romney travels to Washington, D.C., for a fund-raising appearance Thursday that asks for $1,000 to attend, $2,500 to pose with the candidate and $10,000 to join a policy roundtable led by former government officials.

Mr. Gingrich, meantime, will head west to California early next week for eight scheduled fund-raising events. His campaign, which is some $600,000 in debt and has less than $2 million to spend, hopes to raise about $1 million, an aide said. The campaign said it raised $5.5 million in January and hoped to match that this month.

Winning Our Future, a so-called super PAC supporting Mr. Gingrich, apparently has little left to spend. The group spent some $6 million in Florida and more than $3 million in South Carolina, said Rick Tyler, a strategist for the group. That means it has spent most of the $10 million from casino mogul Sheldon Adelson and his wife—the group's two main benefactors. Mr. Tyler declined to comment on the group's finances.

Mr. Santorum now has at least 72 delegates, according to an estimate by the Associated Press, which makes certain assumptions about how some delegates will be allocated. He is second to Mr. Romney, who leads with 112 delegates. Mr. Gingrich has 32, and Rep. Ron Paul has nine.

It takes 1,144 delegates to claim the GOP presidential nomination.

—Danny Yadron, Dante Chinni, Patrick O'Connor and Sara Murray contributed to this article.

Write to Janet Hook at janet.hook@wsj.com and Neil King Jr. at neil.king@wsj.com