Steve Bruce's men looked on course to join Cardiff in the Premier League, but three defeats out of the last four games have seen them spurn two opportunities to seal their fate.
Watford have come up on the rails and forced a final-day decider, with Hull needing to beat the Bluebirds at the KC Stadium to be guaranteed promotion.
If Bruce's men lose again and Watford beat Leeds, then they will be in the play-offs, but Stockdale is confident his side can get over the line.
"It's time for us to show our character, resilience and courage once again," he told the club's official website.
"We've shown it before. My mind goes back to when we had a really poor performance at Bolton and then came back to beat Birmingham at home.
"We know we can bounce back after the defeat last weekend and now it's a case of going out onto the pitch and doing it.
"Everybody here remains positive. When you have a manager like we have, he'll let you know when you've done well and he'll let you know when you haven't and we know what to do.
"There's a lot of people's livelihoods at stake and you can really make a name for yourself if you win promotion. We want to do that for this club."