The Potters entered 2013 looking to push on and cement a top-half standing in the Premier League.
They have, however, collected just one win in 11 and are in danger of being dragged into a basement battle.
Pulis' men remain six points short of the 40-point mark which is widely considered to be enough to secure top-flight safety.
Wilkinson insists Stoke are looking for much more than simply survival, but concedes that they need to start piecing results together.
"It's always frustrating not getting those wins, but hopefully we can get one soon enough and relieve the pressure," he told Sky Sports News HD.
"You would have to ask the fans what they are thinking, but we're all set. Our aim is to finish top-10, so the more results we can get the better.
"The gaffer and the chairman have done unbelievable keeping the club where we are in the Premiership and everyone's fully behind them."