Sen. Elizabeth Warren said Wednesday that heavy super PAC spending in the Massachusetts gubernatorial contest should prompt a federal crackdown on unfettered political spending by outside groups. Corporations and wealthy individuals, Warren argued, “are trying to drown democracy in their dollars. It’s up to us to fight them.”

Warren spoke to reporters briefly Wednesday morning, after watching Martha Coakley concede to Charlie Baker at Coakley’s Somerville campaign headquarters. Coakley’s concession speech was largely spent thanking her campaign supporters, and congratulating Baker, who edged past her in a race that stretched well past midnight Tuesday. But in response to a question about lopsided Republican super PAC spending in the race, Coakley criticized the proliferation of well-funded outside groups spending large sums in political races.

“It’s not a good trend for Massachusetts, or the country,” Coakley said. “The amazing thing is, we almost won, despite all the spending.” When Coakley said she wanted to work with state attorneys general to advance a constitutional amendment banning unlimited outside campaign spending, Warren applauded vigorously.

A series of 2010 federal court decisions enabled corporations, labor unions, and wealthy individuals to raise and spend unlimited sums of money on political campaigns, as long as the fundraising and spending isn’t directly coordinated with campaign committees that operate within the traditional campaign finance regime. The super PACs that the court decisions created have shifted the center of gravity in politics away from candidates, and toward outside political committees.

CommonWealth reported earlier that outside super PACs and labor unions had spent over $20 million on the Massachusetts governor’s race. The sum is far more than the candidates themselves have spent directly, and it’s nearly double what outside groups spent trying to sway the 2010 gubernatorial race. Most of the increase in spending came from the Republican Governors Association. The RGA poured $12.4 million into television ads and mailers attacking Coakley and praising Baker; it spent more money in Massachusetts in the week before Election Day than the Coakley campaign has spent since January 1.

“You can’t get outspent the way Martha was outspent,” Warren said after Coakley’s remarks Wednesday. “It’s running uphill all the time, and that’s what Martha Coakley had to do. She had to run uphill against outside money every single day of this campaign.”

The RGA, Warren said, “came into Massachusetts and said, how much money do you want, Charlie Baker? What’s it going to take to buy this election? And they just kept pouring money in. And that put Martha at a terrible disadvantage. She didn’t have the Koch brothers to turn to. She didn’t have big oil to turn to. And she sure didn’t have Wall Street to turn to.”

Baker, at his own event on Wednesday, downplayed the impact of ads paid for by the Republican Governors Association. “I’ve said all along the voters make their decisions on all kinds of data points,” he said. “I think our message is fundamentally responsible for our victory.”

After meeting with Baker at the State House, Gov. Deval Patrick disputed the notion that the Democratic Governors Association failed to step up for Coakley the way the RGA backed Baker. “The DGA absolutely stepped up for Martha,” Patrick said. The governor said the difference was “the RGA had more money than the DGA.”

A 2014 Massachusetts law requires super PACs to disclose their spending and fundraising in real-time. Disclosure requirements only reach so far, though. Groups like the RGA disclose a portion of their donors in Internal Revenue Service filings. But many national super PACs also shield some of their donors behind political nonprofits that are exempt, under IRS regulations, from public donor disclosure regulations. So Massachusetts campaign finance disclosures show heavy spending by a pair of super PACs funded by the RGA, but don’t identify whose money the RGA is spending.

Warren said Wednesday that Congress could easily pass a law beefing up super PAC disclosure, although she said she’s not optimistic that a House and a Senate controlled by Republicans would do so. The state’s senior senator looks poised to become a vocal antagonist in the new Republican-led Senate; in the span of a few minutes, she pressed the offensive on a higher minimum wage, student debt, and women’s health and economic issues. And, after Coakley’s concession, she indicated that she’s going to use heavy super PAC spending in the governor’s contest to make the case for a constitutional amendment banning unlimited campaign spending. “Look, I want to be clear about this,” she said. “Transparency itself is not enough.”

Jack Sullivan contributed to this report.