Mr Coveney was speaking following the death of a Polish man, who was sleeping rough, from a suspected drugs overdose on a city centre street on Saturday.
He was the third person known to the city's homeless services to die in just over six weeks, and the fourth in almost two months. The latest death sparked criticism of government funding levels and policy measures around homelessness.
Those working at the coalface, including Cork Penny Dinners' Catriona Twomey and Fianna Fáil councillorFergal Dennehy, said it is clear that not enough supports are in place.
But Mr Coveney said anybody who thinks that homelessness and housing isn’t a big issue for the Government doesn’t understand what they are trying to do.
“That doesn’t mean that there aren’t tragedies happening that remind the Government every week of the urgency of the issue," he said.
Source: Eoin English, Irish Examiner, 10th June 2019