The 'Potters' couldn't secure victory over Burnley on Sunday, instead having to settle for a 1-1 draw which sees them four points from safety with three games remaining.
Head coach Paul Lambert blamed a miss chance from Mame Biram Biouf as the "turning point" of the game but Shawcross believes things aren't that simple.
He told reporters: "You can't nail our bad season to one chance.
"We've been sleepwalking into this, we've been disappointing all season so there's a lot of factors that go into the situation we're in and something needs to change and change quickly.
"We knew what we needed to do and unfortunately we didn't. The effort was there, the endeavour was there but the quality was probably lacking. We've just not got that person who can put the ball in the back of the net, and unfortunately we keep conceding late goals."
Stoke's relegation could be confirmed if they lose at Liverpool next weekend, depending on results around them, but given that the 'Reds' have their two Champions League semi-final clashes against Roma either side, it could prove a welcomed distraction for the strugglers to capitalise.
"Obviously they've got two massive games in the Champions League, we're sandwiched in between that so hopefully their focus is away from our game," Shawcross added.
"We've got to win all three. It's difficult but it's not mathematically impossible yet so we go on fighting and we carry on hoping to pick up those three points. Football's a strange sport and it throws up these surprises."