The Londoners are facing the threat of relegation but looked set to secure a crucial victory after Ashkan Dejagah and Fernando Amorebieta had put them 2-0 up, but Nikica Jelavic pulled one back for Hull and Shane Long then scored a late equaliser.
Asked if nerves or naivety were to blame for Fulham's failure to see out the game, Stockdale said: "All of the above.
"When you are anxious to get the 90 minutes over and take the three points, things can go astray.
"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 are 19th in the table ahead of their penultimate game of the season, Saturday's trip to Stoke, but they are only one point from safety.
And Stockdale added: "It is important we pick ourselves up now.
"It is points we need at this stage of the season. We can't change the Hull result now, so we have to go and win our remaining two games.
"Three points against Stoke on Saturday and we are right back in it. If we play anything like we did in the first 75 minutes, we will be okay. We need a few teams to help us out now, as well."
Fulham captain Brede Hangeland has helped them beat the drop in previous seasons and says now is the time for the current squad to deliver.
"This is where, as a player, you really show your character and be accountable," said the defender.
"It's easy enough to play well when you're 5-0 up and cruising at the top of the league, but now it's a bit different and you need strong characters.
"We all know the stakes. It's do or die for us at the moment, so I don't think it will be a problem to motivate people this week."