"I thought we had to settle as a win would get us through and as it turned out that would have been enough."
McCarthy also praised Blackburn's Duff, who capped his display with the third goal and his first of the Finals.
"Some people think his best position is wide left and maybe it is but he gives a different option when he plays through the middle," he said.
McCarthy said his side would not be overawed by their second round opponents - likely to be Spain - who they meet on 16 June.
"People thought we would get beaten in the first two games
but whoever we meet won't be relishing the thought of playing us on Sunday."
Steve Staunton paid tribute to the legions of the Green Army in the Yokohama Stadium.
"We saw all the old familiar banners that we see from back home and everywhere we go," he said.
"They are absolutely unbelievable, they just keep on coming and following us.
"You just had to listen to the noise and see the green around the stadium.
"I can visualise the celebrations back home and just imagine what is going on, and good luck to them all."
Football Association of Ireland chief executive Brendan Menton heaped praise on McCarthy after the result.
He also insisted his decision to send Manchester
United's inspirational skipper Roy Keane back home was justified.
He said: "Mick has done a fantastic job and it was a very difficult decision to make as a manager, but there is no doubt now he made the right decision.
"To come through with the African champions going out of the group - which was a group of death - and come through in second place is down to Mick McCarthy and his squad and the way he set out the team."