English centre-back Shawcross, who praised the Seagulls for their 3-1 win over West Ham last time out, added that a win over Brighton would "lift everyone" at the club.
"It will be a tough game, they got a good win at the weekend, but if we get the points then it lifts everyone and hopefully us out of the relegation zone," the defender told Stoke's official website.
"We're massively disappointed. We want to get out of the situation we're in, so we'll have to fight to get as many points as possible and Brighton is now a huge game for us.
"It's pivotal that we have that battling spirit from now until the end of the season - we need teams to be scared coming to our place. It's up to us to really press teams into making mistakes and getting as high up the pitch as possible. If we do that and get that atmosphere going, then I'm sure we can win."