The biggest game in the midfielder's short career ended in disaster and a 4-0 drubbing in the San Siro.
Wales now take on Finland at the Millennium Stadium still needing just one point to secure a play-off spot.
Simon said: "We think we owe the manager something and we owe the country something, hopefully we can do that. It is up to us to put things right.
"It is good we have another game so quickly, to get things sorted out and not have to wait a few months."
Simon was pressed into service as an emergency right back because of Wales' injury crisis in Milan and could be asked by boss Mark Hughes to play in that role again.
He added: "It was difficult playing a right-back, but I am not complaining, the manager asked me to do a job there and I will do it to the best of my ability.
"I have played their before against Azerbaijan, but they are not Italy and it was a tough task out there against them. It was difficult to live with them, but they would have given problems to a lot better right-backs than me."
Elsewhere, Goran Bunjevcevic's Serbia and Montenegro could do his team mate Simon and Wales a huge favour by taking points off Italy and Milenko Acimovic is in the Slovenian squad taking on the mighty France in Group One.
Simon Davies is determined to put Saturday's drubbing in Italy behind him as Wales face Finland in a crucial Euro 2004 qualifier tonight.