The Potters have won only once in 10 games and Sunday's last-gasp defeat by Newcastle was their third successive loss.
Supporters have been showing their frustration, but Wilkinson told the Stoke Sentinel: "It's understandable but, if we can get a win on Saturday against West Brom, we can push on and get a good finish to the season.
"We need to stick together, work together and get the fortress back at the Britannia. The fans are a massive part of that."
Manager Tony Pulis has been bearing the brunt of criticism from fans, some of whom are unhappy with the Potters' style of play.
The Welshman has received support from his players, and Wilkinson added: "We are the ones who are on the pitch. He cannot play for us, so we are the ones who have to take responsibility."