The Hornets were booed off by their supporters following their FA Cup fourth-round loss to Southampton on the weekend. Watson even had to intervene as Christian Kabasele and Jose Hobelas got into a squabble with the visiting supporters.
But the former Wigan man is confident a win this weekend could turn around Watford's failing season.
"For me, for the boys and everyone involved, it is probably the biggest game of the season," he said.
"[The poor performance at Southampton] Is what you get when you are not winning games and struggling for form, but we have got to keep going and get out of this.
"We can't rely on anyone, and Wednesday is the biggest game of the season.
"If you ask anyone in the Premier League, first and foremost it is about being a Premier League club next year.
"We have got to go to Stoke and impose ourselves and we have to make sure that we leave nothing on the pitch.
"Any of 10 teams could go down and we have to make sure we are not one of them.
"We are in this hole and we as players, as staff, and everyone involved, we have to get out of it."