Bafana kept their hopes of winning their second Afcon title alive by eliminating the tournament hosts Egypt in the Round of 16 on Saturday.
The 1996 African champions had a slow start to the continental competition having recorded two defeats and one victory during their group stage campaign.
Williams feels their poor preparation affected the team's performance as they played only one friendly match, against the Black Stars of Ghana.
“I don’t want to make excuses. Our preparations weren’t good. We only had the game against Ghana," William told the media.
"Other teams played three or four games. As coach Baxter said, we’re using this tournament as preparation. The further we go, the better we will get."
The SuperSport United shot-stopper was surprisingly dropped by Bafana head coach Stuart Baxter ahead of the team's clash with Namibia which South Africa won on June 28.
"It’s part of the game, the coach explained his reason. I didn’t let that keep me down. I stayed positive and mentally strong," he revealed.
"I continued working hard at training. I was prepared when given the opportunity again.”
South Africa will now take on Nigeria in a highly anticipated quarter-final encounter at Cairo International Stadium on Wednesday.