WASHINGTON — In forcing a tense Senate showdown over voting rights, Senator Chuck Schumer violated a cardinal rule of congressional leadership: Don’t go to the floor unless you are certain you have the votes to win.

Mr. Schumer, the New York Democrat and majority leader, definitely did not have the votes to win approval of his party’s voting rights package on Wednesday. He and everyone else in the Senate knew it well before Democrats failed to break a Republican filibuster against the legislation and then lost a bid to overhaul the filibuster rules when two Democrats refused to go along.

The outcome left Democrats disappointed and distressed that they do not yet have a legislative answer to what they see as an alarming trend of Republican-led states imposing balloting restrictions aimed at reducing participation by minority voters.

But as they assessed Wednesday’s wide-ranging debate and solid party unity on voting rights — if not on Senate procedure — Mr. Schumer and other Democrats said they believed they did the right thing even though, for them, it produced the wrong result.

Their view is that Democrats could not identify the new state voting laws as an existential threat to democracy and make voting rights their top priority and then shy from holding a vote because they could not prevail.

In an interview on Friday, Mr. Schumer, far from beaten down, expressed pride in the way Democrats had handled the fight. He said Democratic senators and their allies recognized that such a battle could not be won in a single clash, but could never be won at all if the fight was not joined.

“On civil rights, it is not linear,” said Mr. Schumer, pointing to a positive response from activists who urged Democrats to go to the mat on voting rights even though they were not going to succeed. “You’ve got to keep fighting. And they see that the Democrats really fought for something we believed in, even if we couldn’t win.”

“This issue is different than any other issue,” said Mr. Schumer, who dismissed as ridiculous the criticism that Democrats should have held off when they could not produce either 60 votes to overcome the filibuster or 50 votes from their caucus to unilaterally change the rules and pass the bill. “It’s the fundamental backbone of our country — voting rights. But it’s also the core of our party.”

It was not always a foregone conclusion that Democrats would come up short.

Despite declared opposition to changing the rules from two of their party’s centrists, Senators Joe Manchin III of West Virginia and Kyrsten Sinema of Arizona, Democrats hoped that they could be persuaded that safeguarding the right to vote — and protecting some politically at-risk colleagues — outweighed preserving a signature bit of Senate procedure. After all, many other Democrats who had long been reluctant to tinker with the filibuster had changed their view because of the voting legislation emerging in Republican-led states after the 2020 election.

But it was not to be. Both holdouts stuck firmly to their guns, a refusal to budge punctuated by Ms. Sinema’s loud “aye” vote to uphold the rules.

Republicans remain mystified by Mr. Schumer’s strategy. They cannot fathom why he would want to highlight the divisions between most of his caucus and Senators Manchin and Sinema, provoking grass-roots outrage at two senators he is going to need on other issues as Democrats try to resurrect President Biden’s stalled agenda.

They cannot understand why he would force 47 of his members to join him on record in support of curbing the filibuster in a losing cause, a vote that Republicans will now try to exploit by accusing Democrats of a power grab in pursuit of progressive initiatives such as granting statehood to the District of Columbia and expanding the Supreme Court.

Senator Mitch McConnell of Kentucky, the minority leader, called the debate that ended with the filibuster intact perhaps the most important day in Senate history. He said the vote would haunt Democrats, even though they did not succeed.

“An unprincipled attempt at grabbing power is not harmless just because it fails,” he warned Democrats. “Voting to break the Senate is not cost-free just because a bipartisan majority of your colleagues have the wisdom to stop you.”

Democrats brushed off such talk and said they found the clash cathartic. They said it yielded some benefits, including simply reminding lawmakers that the Senate is still capable of waging an intense and consequential debate. Even some Republicans said the daylong rhetorical battle over voting rights, which brought dozens of senators to the floor to speak, vote and engage in procedural tussling, was a refreshing change from the usual desultory action and phoned-in filibusters.

“It certainly produced the closet thing we have seen to a Senate debate in 15 years,” said Senator Jeff Merkley, Democrat of Oregon and a leading proponent of reining in the filibuster.

Democrats said the political pressure also brought Republicans to the table for discussions about potential changes in the administration of federal elections and the counting of presidential electoral votes to avoid a repeat of the Jan. 6 assault on the Capitol, opening a potential path to compromise.

Mr. McConnell said again on Thursday that Republicans would entertain changes in the Electoral Count Act to close loopholes that Donald J. Trump and his allies tried to use to overturn the election results.

“It clearly is flawed,” he said of the existing law. “This is directly related to what happened on Jan. 6, and we ought to be able to figure out a bipartisan way to fix it.”

Even Speaker Nancy Pelosi, a charter member of the “don’t vote if you don’t have the votes” club, said Mr. Schumer did the right thing in forcing action.

“You had to have the vote,” she told reporters on Thursday, reflecting a view shared by progressive activists who had previously shown some frustration with Democrats.

“There was this legislative dance going on about who would vote for it and this Washington inside political game of ‘We don’t have the votes and we don’t want people to take a stand,’” said Marc Morial, the head of the National Urban League and a former mayor of New Orleans. “It was really important to get everyone on the record and put a marker down.”

Mr. Schumer said Democrats were still considering their future voting rights approach and could break out elements of the legislation for separate votes.

“While last night’s vote was disappointing, it will not deter Senate Democrats from continuing our fight against voter suppression, dark money, partisan gerrymandering,” he said on Thursday. “On an issue this important, not doing everything we could would have been unacceptable.’”