The comments from the country’s top diplomat come despite the EU’s stated support for Iranian citizens’ right to peaceful protest, with the bloc calling only for the end to violence from both sides.
While some individual European countries have joined the US in explicitly backing the protesters, Mr Tillerson lamented a perceived lack of similar support from the 28-nation union.
“We’re disappointed that the European Union has not taken a more definitive stance in supporting those voices in the country that are calling for reform,” he said.
There have been 21 deaths and more than 1,000 arrests as a result of the protests so far, which erupted in Iran’s second largest city Mashhad on 28 December and spread across the country.
Mr Trump has thrown his weight behind the protesters’ attempt to “take back their corrupt government”, pledging “great support” at the “appropriate time” in a tweet.
Despite Mr Tillerson’s comments, the European Union said it was “closely following the ongoing demonstrations in Iran, the increase in violence and the unacceptable loss of human lives”.
“For the EU, human rights have always been a core issue in our relationship with Iran,” read a statement.
“Peaceful demonstration and freedom of expression are fundamental rights that apply to every country, and Iran is no exception.
“In the last few days, we have been in touch with the Iranian authorities. In the spirit of frankness and respect that is the basis of our relationship, we expect all concerned to refrain from violence and the right to expression to be guaranteed, also in light of the statements made by the Iranian Government.”
Iran protests – in pictures
The protests are made up mostly of working class citizens under the age of 25 who are said to be angry at government corruption, a stagnant economy and rising food prices.
Experts also believe discontent has been on the rise since the nuclear deal with the P5+1 in 2015, with many in Iran of the belief that there has been an unfair distribution of benefits throughout the population since the lifting of sanctions.
The P5+1 includes the five permanent members of the UN Security Council – the US, the UK, Russia, China and France – and Germany.
The President has been a vocal critic of the P5+1 deal which was negotiated by his predecessor Barack Obama and some observers think he might use the unrest in Iran to follow through on one of his campaign promises and tear it up.
Mr Trump has sent mixed messages about the European Union in the past.
In July 2017, the President took to Twitter to criticise the EU for being “very protectionist with the US” and said that it had to “stop”. This came after he claimed to be working on a “major trade deal” with the UK.
And in January 2017 during an interview with Michael Gove he praised the UK’s Brexit decision and predicted the EU would continue to break apart as a result of the refugee crisis.
However, a month later in February Trump hailed the EU as “wonderful” and said that he is “totally in favour of it”.
Mr Tillerson also said that the administration was working with key members of Congress on a legislative fix that could enable the US to remain in the Iran nuclear deal.