Graffiti warning off inspectors has appeared close to ports in recent weeks.
Police have insisted there is no evidence loyalist paramilitaries are involved in the sinister campaign, instead blaming disgruntled individuals and small groups.
Cabinet Office minister Michael Gove and European Commission vice president Maros Sefcovic will hold a virtual meeting with DUP leader Mrs Foster and Deputy First Minister Michelle O'Neill to discuss the ongoing furore over the protocol on Wednesday.
Speaking on BBC Radio Ulster’s Good Morning Ulster, Mrs Foster stated that the DUP was representing the interests of the people of Northern Ireland through its plan.
Mid and East Antrim Borough Council voted to withdraw staff from the port of Larne, while former Agriculture Minister Edwin Poots made the same decision before he stepped down due to health issues.
“Do you think the DUP in the council, where they only have 16 members [would go against that decision]?” said Mrs Foster.
“The fact that all of the council group leaders, including Sinn Fein, agreed to suspend the operation of the workers at the port of Larne on the advice of officials. I just find that unbelievable.
“The next thing is a government department is being accused, again on official advice, to deal with this issue but yet again it’s the DUP’s fault.
“I have to say, I think that is absolutely incredible this morning.”
Mrs Foster denied that she was undermining the PSNI’s response to the threats made to port workers and said her party is engaging with police on the matter.
“It’s not just about a bit of graffiti on the wall, although I note when the graffiti was mostly on DUP offices it wasn't really a problem it was only when other offices were targeted it seemed to be a problem,” she continued.
“Secondly, just because it’s not from one of the mainstream loyalist paramilitaries it doesn't make it any less of a threat.”
Mrs Foster added that politicians such as Mr Coveney were the reason why the protocol was introduced in the first place as she accused them of putting north-south trade ahead of east-west trade.
“It needs to be fixed so let us in a calm and firm way - to use Simon Coveney’s words - bind those relations instead of whipping up that the DUP are trying to cause tensions,” she said. “That is not the case.”
Mrs Foster insisted constitutional politics was the only way to deal with the issue.
“That is what the five-point plan is about and I hope other unionists can join with us in terms of moving things forward but it is so important that people understand that constitutional politics has to work here in Northern Ireland,” she said.
Meanwhile, deputy First Minister Ms O’Neill told the BBC that the EU made a “huge mistake” after it announced its ill-fated plan to trigger Article 16 but believed the DUP used it as an opportunity to “attack the protocol”.
She said there are a range of issues which must be identified in relation to Brexit but it was “wrong” to point out that they are a direct result of the protocol.
However, Ms O’Neill added that some problems were a “direct consequence of the hard Brexit policy that was championed by the DUP” and called their five-point plan “reckless”.