The Potters' perilous position has piled the pressure on manager Mark Hughes, with some fans calling for him to be sacked. However, Adam believes it is the players that must take responsibility for the team's record of five defeats in their last seven league games.
"We're in the mix now," Adam told the club's website (www.stokecityfc.com). "We are down there fighting for survival, and we need to find some character to get us out of this mess.
"We need to stand up and be counted, because as a group of players, we are the ones who have put ourselves in the situation we're in."
The Scot said that Stoke should prioritise the league over FA Cup fixtures but urged the team to get a much-needed morale boost by beating Coventry City in the cup competition on Saturday.
"League form must take priority, but when you're in this situation, you just have to win games. We have to look at ourselves, and get a win in the next game," Adam added.
"The players have to keep going, and keep up the fight... As a team, we need to pick up points as soon as possible, and come the end of the season, hopefully it will be enough.
"Coventry City on Saturday is not going to be an easy test. They are going OK in League Two (fourth tier), so it is going to be a difficult game."
Stoke return to league action with a trip to Manchester United on Jan. 15.
(Reporting by Aditi Prakash in Bengaluru; Editing by Christian Radnedge)
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