However, McCullough told BBC News NI’s Good Morning Ulster programme while the people he represented were not anti-Irish, Irish was not “part of their identity”.
Unionist councillors are now expected to submit a call-in, a mechanism where a decision of the council is reviewed.
TUV deputy leader Ron McDowell added that the Irish language was being “weaponised, politicised and forced on communities that don’t want it”.
“There are huge areas of the city that don’t have an Irish population, don’t identify as Irish and why should we therefore have Irish thrust upon us?”
The proposed new 18-page policy, which has been published on the council’s website, was approved by a Belfast City Council committee in September, and was ratified on Wednesday night.
Sinn Féin, the Social Democratic and Labour Party (SDLP), Alliance, People Before Profit and the Green Party voted in favour of adopting the policy.
The DUP, Ulster Unionist Party (UUP) and Traditional Unionist Voice (TUV) voted against.
DUP leader Gavin Robinson told BBC News NI: “If this is a shared city, we don’t stand in the way of anybody trying to engage their interest to speak Irish, but nor do we want it foisted upon the vast majority who have no interest or knowledge.”
