The 32-year-old defender returned from the Republic of Ireland's campaign in Poland and Ukraine with a problem which required surgery, and is currently working his way back to fitness.
Villa last month expressed their disappointment regarding his medical treatment while with the Republic team, but have now issued a clarification . A club statement said: "We wish to acknowledge that Richard Dunne received the highest standard of medical care before and during the Championships and apologise to those involved in providing his treatment if any other impression was erroneously given."
Villa made their initial comments when confirming that both the defender and striker Gabriel Agbonlahor would miss the start of the new season through injury.
It said: "Richard Dunne will... be out of action for six to eight weeks, having undergone a procedure on a groin injury which he sustained and was not dealt with during the European Championships."
Dunne played the full 90 minutes in each of Ireland's three games at the finals, finishing on the losing side on each occasion against Croatia, Spain and Italy as Giovanni Trapattoni's men bowed out of the competition at the first hurdle.
He has since indicated his intention to continue his international career in talks with the Italian, although his injury means he will miss Friday's opening World Cup qualifier in Kazakhstan.