The comments come two days after the Republican president-elect met the country's leading intelligence agency chiefs, who told him that Russian President Vladimir Putin directed a vast cyberattack and leaking campaign aimed at helping install him in the White House.
Although Trump accepted the possibility that Moscow was involved in hacking US targets including the Democratic National Committee (DNC), the president-elect has held fast to his rejection of the intelligence community's conclusion that Russia interfered in the election, and has called the accusations part of a "political witch-hunt" against him.
Trump's senior aide Kellyanne Conway repeated that line on Sunday, telling CNN that "any attempt, any aspiration to influence our elections failed."
"They were not successful in doing that, and it's a very important point," she said of the Russians, blaming Democrats instead for allowing their accounts to be hacked.
"We're talking about this because we had embarrassing leaks from the DNC e-mails," she said. "There were no fireworks in that report because there was no firewall at the DNC."
Trump's Democratic rival Hillary Clinton lost the election "all on her own," Conway added.
"We didn't need WikiLeaks to convince the American people they didn't like her, didn't trust her or find her to be honest," she said of the website that posted the documents.
Conway also repeated Trump's accusation that the White House leaked information about the intelligence before it was shared with Trump on Friday.
"You can't have people in positions of keeping us all safe and knowing classified information or intelligence information, we can't have them leaking to the media," she said.
"That should really infuriate Americans today, that people who possess this information are sending it to the media ahead of the president-elect receiving the information."
Trump has made repeated calls to improve relations with Moscow. "Having a good relationship with Russia is a good thing," he tweeted on Saturday. "Only 'stupid' people, or fools, would think that it is bad!"
Asked whether that meant Trump would not take action against Russia for hacking, White House chief of staff-designate Reince Priebus told Fox News on Sunday that the president-elect would order the intelligence community to make "recommendations."
"The recommendations will be discussed and actions may be taken," he said. "But I don't think there's anything wrong with trying to have a good relationship with Russia and other countries around the world."