The Reds earned their second point of the season and secured their first clean sheet under manager Oliver Glasner.
Forest also created enough opportunities to claim victory, although Williams saw a second-half goal ruled out by VAR.
Fresh from signing a new contract last week, the defender is confident Forest can build on the performance.
“We take the point and the clean sheet. There were plenty of positives that we can take,” Williams told the club website.
“There are a lot of new things the coach has brought to us. With this team, the mentality and desire will never go, and I think we showed that.
“Every player left everything out there on the pitch, which is why it’s so frustrating that we didn’t get the three points.
“We move on now, take the positives and look to the next game.”