Williams told BBC Sport: "We were very focused and did what we came to do. Personally I really wanted to work harder than my opponent and prevent anything getting through on goal.
"We want to be a team with character and fight, that is the only way that you can get anywhere in the Premier League. There are no stars here, the team is the star. That is one win, but we need to go again."
The game was Louis van Gaal's first Premier League match in charge of Manchester United.