Evans believes Dalglish will be suffering as much as any fan after the recent run, which has left Liverpool 34 points off of the top.
"Nobody will be hurting more than Kenny," he told the Liverpool Echo. "I hear people say they don't listen to the critics, but in this day and age that is almost impossible. The media coverage of football is 24/7 now, there is no escaping it.
"He was the fans' choice as manager when Roy Hodgson left. I don't think there was a fan around who didn't want Kenny in.
"As manager of Liverpool, there are high expectations. You wouldn't want it any other way, either. You wouldn't want the players and the manager to be happy with the way things are going.
"The league table doesn't lie. It is up to the players and the manager to make sure it reads a little better sooner rather than later."