The Potters, who sit four points above the drop zone, host Aston Villa on Saturday and Shawcross wants plenty of noise at the Britannia Stadium for the meeting with the 18th-placed Villains.
"It's pretty well known how good the Stoke fans are when they are roaring and behind us. It's massive and hopefully we can push on after that," he told the Staffordshire Sentinel.
"I think it would probably take 37 points (to stay up), so we need to get to that then hopefully push on.
"We need to be calm, collected and make sure we do our job. Our home record is fantastic. In recent times we have had a few losses, but throughout the seasons it had been very good.
"We have some tough away games but also some good home games from which we can pick up points. It's going to be difficult but we can do it."