The shot stopper attempted to play the ball out from the back with Sundowns leading the German side 1-0, but his pass was intercepted by midfielder Felix Nmecha for the equaliser.
Sundowns went on to lose the FIFA Club World Cup group stage tie at the TQL Stadium in Cincinnati, Ohio, by 4 goals to 3 and have one more fixture to go against Fluminense on Wednesday.
Although the Brazilian number 1 is aware that the mistake was costly, Williams said this is the price that they sometimes have to pay for the style of football they play.
"Of course, it's not nice to concede a goal like that, but we are a team that takes risks. When I received the ball, I saw Tebza [Mokoena] there, but he got a call from Marcelo [Allende] to move away as soon as I passed the ball, so it was just one of those unfortunate situations," explained Williams.
The Bafana Bafana captain felt they also had themselves to blame for not punishing Dortmund when they had the chance.
"At this level, if you make mistakes, you will be punished, and unfortunately, we had to learn the hard way.
"I think all of their goals were errors from us, and where we come from, we get away with it. We shouldn't be disappointed, I'm proud of the boys for playing our football and displaying our identity," said the Sundowns shotstopper.
Sundowns got off to an ideal start in the tournament when they beat Ulsan HD 1-0 to open their campaign a few days prior, and Williams says coach Miguel Cardoso did a good job trying to lift their spirits following the Dortmund defeat.
Up next for Masandawana is their third and final group clash against Fluminense on Wednesday.