Williamson was part of the Newcastle side beaten 4-0 by Tottenham on Wednesday, with Alan Pardew's side taking just four points from a possible 24, finding the net in just one of their last eight Premier League games.
Pardew accused his charges of not giving "life and limb" in Wednesday's defeat.
Williamson acknowledged the anger among fans at the current run of form but insisted the players are feeling the pain as well.
"It might have come across to the fans that there was no heart, and that’s a disappointing thing," he told The Northern Echo.
"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.
"But 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."
Newcastle sit ninth, nine points clear of Swansea City in 10th, following a defeat in which Pardew stated his side were "dominated from start to finish".
Williamson confirmed Pardew had made no secret of his anger at the performance, adding a reaction against Aston Villa on Sunday is paramount.
"We've seen that side to him before," Williamson continued.
"Every now and again, when it is necessary, he tears into us, but there needed to be some harsh words said because he felt it wasn't good enough from the players out there on the pitch.
"First, you do it for yourself, then the manager and the fans and the club. That's where it builds from, but yeah, we have let the manager down.
"We have let the fans down and we have let ourselves down, so it is all about getting back to the basics now."