The Potters were beaten 3-1 by Aston Villa at the Britannia Stadium on Saturday and the Scotland international has admitted that the character of the group will be tested
Paul Lambert's rejuvenated team closed the gap between themselves and their opponents to only one point with victory at the Britannia Stadium on Saturday.
The defeat leaves Stoke lying just three points above the drop zone having played one game more than 18th-place Wigan.
"We're in the relegation scrap now," Adam told reporters after Matthew Lowton's late goal had earned Villa all three points.
"It's about characters and we will see how good the character of the group is. That's got to be the question now and we have to step up to the mark.
"You need hard work. If you don't have that, we are going to be sucked into it."
Stoke face the daunting task of overcoming Manchester United in their next match but Adam insisted that they should not rule out springing a surprise on home turf despite their poor form.
"Man United will be going for the title, but we're at home and if we can get our confidence up for the game, who knows?" the Scotland international said.
"But it's going to be a tough match for us. We need to pick up points wherever. We need to start doing what we did at the start of the season.
"Getting after teams, enforcing our game upon them and hopefully we can starting getting some positive results."