The Trotters travel to Upton Park tomorrow hoping to register their third successive Premier League victory in east London.
Avram Grant's West Ham crashed to a 3-0 defeat at Aston Villa last Saturday and Knight knows their fans will grow restless if they struggle again.
"The crowd will get behind them but their fans demand a lot," Knight told Bolton's official website.
"If we can play our type of football, press them and get them on the back foot, then hopefully we can make the crowd turn.
"Maybe then one or two their players' heads will drop and we can capitalise by getting one or two goals.
"West Ham will obviously want to do better than they did last week as they made a poor start against Villa.
"For us we want to do better than our draw against last weekend and I don't see why we can't come away with the points we want.
"Although we believe it was a good performance against Fulham you always want to better yourself.
"If we do that against West Ham then we believe we'll come out on top."
Bolton have lost just twice at Upton Park in the last decade and the ground gave manager Owen Coyle his first away win as manager, a 2-1 triumph in March.
Former Fulham centre back Knight, however, refuses to be swayed by that record.
"At times it's not good to look at previous form because it's about what happens on the day," he said.
"Sometimes form can go out of the window and we know it will be a tough match because it's West Ham's first game of the season.
"We did everything right there last season. We defended well and scored a good couple of goals.
"Maybe they could have got something right at the end but they didn't and we showed good fighting spirit.
"We need to have that throughout this season, and not just against the teams in and around us but in the big games as well."
Bolton kicked off the new Premier League campaign with a goalless draw with Fulham at the Reebok Stadium and Knight was delighted with his team's defensive display.
"It was a good start to the season for us against Fulham, every player did their bit," he said.
"We kept a clean sheet - last season we didn't do that until the second half of the season, so that was pleasing.
"It would have been nice to win our first game of the season. It wasn't meant to be but it's a great platform to carry on.
"Pre-season went well and we have two players in every position so the boys know they have to play well to keep the shirt."