The Secretary of State won 49.9 per cent of the vote, with Mr Sanders – a senator from Vermont – finishing with 49.6 per cent.
But initial rounding of the results put them on half each, causing Mr Sanders to claim a “virtual tie” with his more prominent rival.
His aides contacted The Hill, an American political newspaper, to claim that 90 caucus voting sites were inadequately staffed by “impartial” chairmen and women.
Relying on possibly conflicting figures from partisan aides could lead to further disputes over the result, but the Iowa Democratic Party said results would not be taken from campaign teams.
Instead of using paper ballots for caucuses, the Democrats invite supporters to physically cluster together and be counted by precinct chairs – a practice that makes re-counts impossible.
“You will have the ability to stand with your neighbours in support of your preferred candidate, or to declare yourself as uncommitted,” the official caucus website states.
“This is as simple as walking toward the corner of the room that’s been reserved for your candidate.”
Footage from election night showed some votes between Mrs Clinton and Mr Sanders being so close they were decided by a coin toss, which is the Democrats’ official method of deciding a tie.
The Iowa Democratic Party fended off accusations of unfairness, acknowledging the caucus was “historically close”.
Hillary for America’s Iowa state director, Matt Paul, said there was “no uncertainty” over the results and no missing information.
“After thorough reporting – and analysis – of results, there is no uncertainty and Secretary Clinton has clearly won the most national and state delegates,” he added.
“Statistically, there is no outstanding information that could change the results and no way that Senator Sanders can overcome Secretary Clinton’s advantage.”
Democrat presidential candidates
Democrat presidential candidates
1/5 Hillary Clinton
If Americans are fuzzy on the other Democrat runners, they may feel they already know quite enough about Ms Clinton, who has gone from US First Lady to Senator to Secretary of State, navigating serial media maelstroms along the way. It's exhausting to enumerate them (Whitewater, Monica, Benghazi, the email server). She cried in New Hampshire in 2008 yet failed to stave off Barack Obama. Now she's after the nomination again. She has had a lousy campaign so far, yet this remains hers to lose.
2/5 Bernie Sanders
The self-described Democratic Socialist Senator from Vermont is technically an Independent on Capitol Hill but almost always votes with the Democrats. Since jumping into the nomination race, he has stunned probably even himself with the huge crowds he has drawn and his success at raising money from grassroots supporters.
3/5 Marton O'Malley
Mr O'Malley, the Governor of Maryland until the start of this year and before that Mayor of Baltimore, seemed well placed to challenge Ms Clinton. He has a strong record of progressive accomplishments in his state. So far, however, while his speeches are well received, his polling numbers have remained pathetic.
4/5 Lincoln Chafee
Mr Chafee, who shod horses as a young man, was a Republican US Senator for Rhode Island who defied his party and voted against the Iraq War. In 2011, he was elected as the state's governor as an Independent. Now he's running as a Democrat. His pet project? He wants the US to say goodbye to Fahrenheit and go metric.
5/5 Jim Web
Former Virginia Senator Jim Webb has dropped out of the race for the Democratic presidential nomination, although he has hinted that he might still run as an independent.
Mrs Clinton has been considered the Democratic Presidential front-runner but the result raises doubts over her ability to unite the party.
Her campaign against Barack Obama also ran off the rails in Iowa in 2008 and her campaign will be hoping that the state caucuses to follow will show stronger support.
But Mr Sanders has been leading in opinion polls in New Hampshire, which will be the next state to hold its primary on 9 February.
Additional reporting by Reuters