Democratic Senator Al Franken told Yahoo News: "I think she has a right to analyse what happened, but we do have to move on."
Mrs Clinton this week faulted Democratic National Committee (DNC) voter data as "mediocre to poor".
She has also blamed the FBI, Russia and media.
Minnesota Senator Franken said on Thursday: "We have to move on by proving we are the party that cares about a lot of the people who voted for Donald Trump."
Mrs Clinton, speaking at a conference in California on Wednesday, said: "I take responsibility for every decision I make - but that's not why I lost."
She said the Democratic party did not help her once she was anointed their White House candidate.
"I get the nomination, so I'm now the nominee of the Democratic Party," she said.
"I inherit nothing from the Democratic Party. I mean, it was bankrupt.
"It was on the verge of insolvency. Its data was mediocre to poor, non-existent, wrong.
"I had to inject money into it."
She added: "I also think I was the victim of the very broad assumption that I was going to win."
But Andrew Therriault, former DNC director of data science, lashed out at Mrs Clinton in a series of tweets that have since been deleted.
"DNC data folks: today's accusations are f****** bull****, and I hope you understand the good you did despite that nonsense," he wrote.
He also wrote that the battleground swing states of Michigan, Wisconsin and Pennsylvania, all of which Mrs Clinton lost, never looked "even close to safe".
The Clinton campaign has been criticised by political experts for not campaigning more frequently in those crucial swing states.
"Her team thought they knew better", Mr Therriault said.
President Donald Trump reacted to Mrs Clinton's complaint by pouring scorn on his old foe.
"Crooked Hillary Clinton now blames everybody but herself, refuses to say she was a terrible candidate," he tweeted. "Hits Facebook & even Dems & DNC."