Offering advice on the current political situation during a talk at Knock Methodist Church in Belfast last Friday, the ex-DUP leader warned against allowing “the most vociferous voices in your party lead you”.
In an interview on BBC’s The View yesterday, Mr Robinson denied that his comments were aimed at his successor Mrs Foster.
He insisted he was not criticising anyone in particular, adding: “It’s not an attack on the leadership. It is an obsession with some people in the press who want to get at Arlene.”
When asked who the “most vociferous voices” remarks referred to, he replied: “I am talking about people in every party. There are always people who are passionate and outspoken in politics.
“Generally when people are satisfied with the line you take, they don’t speak out. It is those who are against your line or have misgivings about it who will speak out most loudly.
“You have to have a proper consideration of exactly where the party stands on these issues rather than listen to those who talk the loudest.”
Mr Robinson was speaking to the BBC at New Haven in Connecticut in the USA, where he is attending a conference to mark the 20th anniversary of the Belfast Agreement.
He also played down comments by the DUP MP Sammy Wilson, who last week told the News Letter that business and farming leaders were being used as “puppets” by the government in a bid to promote Theresa May’s Brexit deal.
Mr Robinson said his reaction when he heard the remarks was: “There goes Sammy.”
He described the East Antrim MP as “probably one of the best commodities any political party could have”, adding: “He has a great way of connecting with people, but like everybody else he will say things that others wont agree with.
“He is very passionate on the Brexit issue and says it as he sees it.”
Mr Robinson added that business leaders were “not anyone’s puppets”, and felt the spat between his former party and business leaders had “not damaged the DUP brand”.
On Brexit, Mr Robinson said his party is right to oppose the PM’s draft withdrawal deal.
He said he was not convinced it is the “only deal”, adding: “How often were we told that during the lifetime of the Belfast Agreement, that this was the only show in town?”
On the ongoing political vacuum at Stormont, Mr Robinson felt that while Sinn Fein has wanted to collapse the institutions back at the start of 2017, he now believes the party “would want to get back into the Assembly, as does the DUP”.