City are currently 13th in the Premier League but just four points above the relegation zone after claiming just six points from their last 12 games.
Defender Shawcross, 25, is keen for his side to try and reach the 40-point mark as soon as possible and believes a passionate home crowd at the Britannia Stadium will assist them.
"It's pretty well known how good the Stoke fans are when they are roaring and behind us," Shawcross told the Staffordshire Sentinel. "It is a season-defining game now on Saturday. It's massive and hopefully we can push on after that.
"I think it would probably take 37 points (to stay up), so we need to get to that then hopefully push on.
"Maybe it will be a bit less or more, but we want to get to 40 and then push on from that. It is going to be difficult but they are all winnable games.
"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.
"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 will go there with hope, hope the fans get behind us, roar us on and hopefully we'll get a massive victory."
Jon Walters agrees that Stoke will be up for the fight against Villa.
"It is a big game, but we've had good results against Villa down the years and we've got to go in there all guns firing," said the striker.