The Cottagers had got themselves into a commanding 2-0 lead before two late goals saw Hull claim a share of the spoils.
The result means that Fulham are now one point adrift of safety with two games remaining.
"When you are anxious to get the 90 minutes over and take the three points, things can go astray," Stockdale is quoted as saying by BBC Sport.
"There was a lot of tension in the ground and we did things that we would not normally do at home. That was our downfall."
Fulham continue their Premier League campaign on Saturday when they travel to Stoke City.