Eurogroup head to US: If you want billion-dollar fines to stop, sort out your taxes

For its part, Ireland has opposed the European Commission's ruling on concerns that it would jeopardize its policy of wooing foreign businesses to relocate there, as well as interfering with the country's' sovereign right to set tax policy.

In response, Apple chief executive Tim Cook has slammed the decision as "total political crap" and "completely unfair,"

However, Dijsselbloem dismissed the controversy, telling CNBC that there was a new mood in Europe.

"The bottom line is, and the big companies have to realise this, times are changing and new times will ask them, make them, pay taxes in a fair way," he said.

"Where they make their profits, they must pay their taxes to a fair amount, a fair share and I think for too long they have been able to get out of that and it has to stop," the official told CNBC.

"I think to my citizens I cannot explain why they should pay their fair share and the large companies do not."