The Magpies slumped to a 4-0 defeat against Tottenham Hotspur on Wednesday.
Williamson told The Northern Echo: "It might have come across to the fans that there was no heart, and that's a disappointing thing.
"Sometimes, the fans can be a little bit unfair, but you can't say that over the past few games. They are justified, and we completely understand their anger and upset.
"Believe me, the players in there are feeling exactly the same. Now, it is all about getting that reaction and making sure we can convey our spirit and fight against Villa, when we've got to bounce back."