The Sinn FÃ©in president's comments come after DUP leader Arlene Foster chastised the Taoiseach Enda Kenny for saying he believed the EU was stronger with the UK as a member state.
The first minister said it was a matter for voters in Northern Ireland and not the Republic of Ireland.
Mrs Foster was responding to comments made by Enda Kenny on Monday.
Mr Kenny said that it would create "serious difficulties" for Northern Ireland if the UK was to leave the EU.
Speaking at a book signing in west Belfast, Mr Adams said: "Protestations from unionists about the Taoiseach's intervention on the Brexit issue are entirely self-serving.
"The Taoiseach is fully entitled to comment on any matter, on any part of this island.
"On the issue of Brexit, our big objection is that the people on this part of Ireland would be dragged behind what ever decision the people in Britain make and it's a matter for them what decision they make.
"If they decide to leave, it would have effects here, it would have consequences here, but we who live here, I don't think any of us want to see a land frontier."
The Irish government has made it consistently clear that it does not want to see Britain leave the EU.
Its main concern is economic - the UK is Ireland's biggest trading partner and the two countries trade over 1bn euros (Â£760m) of goods and services every week.
Ireland's other concerns include the potential impacts on Northern Ireland and the wider British-Irish relationship.
A referendum on UK membership of the EU must be held by the end of 2017, though it could be as early as June this year.
Gerry Adams has told an audience that the forthcoming referendum on the EU matters to people on both sides of the border.