Police stand guard as Scottish independence supporters clash with pro-union campaigners at a Friday reconciliation rally in Glasgow, a day after the referendum. Zuma Press

GLASGOW, Scotland—Though Scotland has settled its independence referendum by choosing to stay in the U.K., rifts created in the fiercely contested vote remain.

"The Scottish people got it wrong," said Susie McIntyre, a 40-year-old stay-at-home mother in central Edinburgh over the weekend, who was one of the 45% of voters who had cast a ballot for independence. "The people who voted for the union—they should've taken the bull by the horns and stood up for what they truly believed."

Senior politicians and other public figures are now waging a campaign to mend such divisions and soothe resentment toward the British government.

Former Prime Minister Gordon Brown of the opposition Labour Party sought to smooth over tensions in a speech in the Scottish town of Dunfermline on Saturday, urging his fellow Scots to throw away their "yes" posters for independence or "no" posters against it. In the streets of Edinburgh, many of the blue posters still hang in windows.

"Consign these to the history books," he said. "No longer think of yourselves as 'Yes Scots' and 'No Scots,' but all of us Scots."

A reconciliation rally in Glasgow on Friday suggested that could take some time. As separatists and unionists gathered in the city's George Square for the event, the mood was somber, despite efforts by a musician and a handful of speakers to liven the crowd.

Within hours, it had soured. Shouting between groups of people in the rival camps erupted and a flare was set off, prompting police to intervene in what authorities described as "ugly scenes." Authorities said they arrested 11 people on a number of public-disorder offenses, including vandalism, though no one was injured.

The U.K. government's most senior minister in Scotland, Alistair Carmichael, acknowledged that the campaigns leading up to the vote had fractured relationships and had some ugly moments—such as the online vilification of Harry Potter author J.K. Rowling, a prominent supporter of the pro-union camp.

Speaking to reporters on Friday, Mr. Carmichael told Scots on both sides to put the referendum and its occasional tensions behind them. "We have to acknowledge these moments and park them. We can't burnish our grievances in the way that Scots sometimes have a tendency to do."

Political recriminations have begun, too. Scottish National Party leader Alex Salmond, who announced his resignation on Friday, told the British Broadcasting Corp.'s Sunday Politics program that the U.K. government had tricked "no" voters into rejecting independence with its last-gasp offer of greater powers for Scotland.

The SNP, which had led the pro-independence charge, criticized politicians in the U.K. Parliament at Westminster on Saturday for failing to deliver on its promise to start the process of transferring more powers to Scotland the day after the Thursday referendum. British Prime Minister David Cameron, as part of efforts to woo voters, had in the final days of the referendum campaign promised give Scotland more say over tax and spending.

A spokeswoman for Mr. Cameron said Sunday that the government would move forward with those commitments. Mr. Cameron has set a November deadline for agreeing on new powers over tax, spending and welfare and said he wants legislation to be drafted by January.

People in Scotland have decided against independence, with 55% voting in support of continuing the union. So what happens now? WSJ U.K. Editor Cassell Bryan-Low discusses. (Photo: Getty)

Even Queen Elizabeth II, who typically remains quiet on political matters, took the unusual step of intervening.

In a statement issued by Buckingham Palace on Friday, she said she recognized the results had led to conflicting emotions among family and friends. But she urged people to settle their differences.

"I have no doubt that Scots, like others throughout the United Kingdom, are able to express strongly held opinions before coming together again in a spirit of mutual respect and support, to work constructively for the future of Scotland and indeed all parts of this country," she said.

On Sunday, Edinburgh's St. Giles' Cathedral hosted a special reconciliation service focusing on the common purpose in Scottish society.

Matthew Flinders, a politics professor at the University of Sheffield, said it might take time for Scottish nationalists to come to terms with the result. But, he added, he didn't expect it to see any "long-term fissures" between those who voted "yes" and those who voted "no."

Stephen Boswell, a 51-year-old chef from Dunoon, Scotland, said he was heartbroken that Scotland chose to stay in the U.K. but added that he wanted society to move forward. "We came up here today for unity," Mr. Boswell said, speaking at the Friday rally in Glasgow, Scotland's most populous city. "We want to bring people back together again."

But Paul Docherty, a 33-year-old musician in Edinburgh, said he was devastated that Scotland had rejected independence and that it would take time for resentment within society to fade. He said he had little hope that the U.K. government would follow through with its promise to give more power to Scotland.

Another pro-independence supporter, Roddy McNairn, a 47-year-old chef from Loch Lomond, stood at the Glasgow reconciliation rally with a Scottish flag draped around his shoulders. "We're a bit deflated," he said. "But, get united, get stronger, and get on with it."

Write to Jenny Gross at jenny.gross@wsj.com, Cassie Werber at cassie.werber@wsj.com and Jason Douglas at jason.douglas@wsj.com