The EFDD group were unable to secure a vice-president position in parliament and are not represented in any of the committee chair positions.
Speaking at a press conference on Tuesday during the Strasbourg plenary session, the two criticised the lack of democracy in parliament and vowed to ensure that their voices are heard.
UK MEP Helmer explained, "The custom and practice which has been long established… is that the De Hond't system is applied so that committee chairmanships, and indeed the vice-presidents of the parliament, are in some sense representative.
"The European institutions in my experience are characterised by a vast contempt for the voters," he said, adding, "That is best illustrated in fact by the reaction to the successive referenda in different countries where you have what I like to call 'biased finality'.
"The European institutions in my experience are characterised by a vast contempt for the voters" - Roger Helmer
"If you get the wrong answer from the institutions point of view you are simply told to keep voting and voting and voting until you get the right answer. When you get the right answer the matter is closed."
He said that UKIP have the "largest UK MEP delegation in Brussels", and that the Five Star Movement also received a "substantial" share of Italian votes.
"What it amounts to is that all those millions of voters who voted for parties that take a Euro-critical stance have simply been side-lined and ignored, and this is a determined effort by the larger groups behind closed doors to have an exclusion policy where alternative views are not listened to," argued Helmer.
"That is not democratic, and, what's more, it is dangerous because if the people come to recognise that their so-called democratic institutions have no place for dissenting opinions they will look for alternative ways of expressing themselves," he warned.
He went on, "This isn't an anti-EFDD particularly movement, this is an anti-small party and a consolidating of the larger parties in a position of control.
"In fact the Greens have suffered as well and are concerned about it, and the ECR itself lost a potential vice chairmanship of a committee as a result of exactly the same activity.
As for the lack of representation in parliament, Helmer said, "We are accepting it in the sense that we know we haven't got those appointments that we wanted to get, but we are also trying to draw the attention of the public across Europe to the way things are done in Europe and the profoundly anti-democratic nature of these institutions.
"So in a way our opponents have presented us with an opportunity to make these points.
"They've come out into the open and said we don't… care about democratic representation of the people, we are going where we are going whether you like it or not.
"That is the authoritarian approach we are facing... we will get further support from the public as a result of the behaviour of the groups who claim that this is a Europe of values based on the rule of law," he complained.
"We will get further support from the public as a result of the behaviour of the groups who claim that this is a Europe of values based on the rule of law" - Roger Helmer
And as for how the EFDD plan to react, Helmer said, "One of the things we’re going to do is to appeal to the court of public opinion, to these many millions of people who voted for UKIP in the UK, for the Five Star Movement in Italy and for other related parties in other parts of Europe.
He continued, "We are still going to speak up, we've lost the formal advantage of certain vice-chairmanships of committees that we believe we ought to have had, and a vice-presidency of the parliament, but of course we still have a voice and a vote and we shall exercise it.
"So we are making huge progress as a Euro-critical political movement in my country, in Italy and across Europe as a whole, and I think these rather grubby devices that the large old parties are using to try and exclude us, they are measures of desperation.
"In the end people will drive the agenda and we are with the tide of history," he finished.
Borrelli, the group's co-chair, also blasted the actions of the parliament, saying, "If this is the democracy of this parliament, then my concept of democracy is a different one.
"We're going to fight to get what we're entitled to, and we're certainly not going to be silenced with these very petty political means" - David Borrelli
"These elections have basically tried to sideline a group that people don't like. Our voice has been silenced in a way that has never been done before in the European parliament," criticised the Five Star Movement member.
"We're going to fight to get what we're entitled to, and we're certainly not going to be silenced with these very petty political means," he declared.
"I think that this coalition, this majority last Monday signed its death knell. If our dissenting voice is not listened to, but it's excluded that probably means they're too scared.
"It clearly means that too many people today in Europe are Eurosceptical and rather than confronting the problem they're trying to sweep it under the carpet," said the Italian MEP.
"That's what has happened here, but I think our role is to speak more and more loudly so that we get heard," he concluded.