Goals from Ashkan Dejagah and Fernando Amorebieta had put the hosts in the driving seat at Craven Cottage, but the Tigers hit back through Nikica Jelavic and Shane Long.
The point was not enough to move Fulham out of the bottom three and, with a trip to Stoke looming before the final-day visit of Crystal Palace, goalkeeper Stockdale has pinpointed where they went wrong last weekend.
When asked if it was nerves or naivety that allowed Hull back into the game, Stockdale replied: "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."
With Sunderland winning 4-0 at home to Cardiff on Sunday, Fulham now sit 19th in the table but just one point from safety.
Stockdale, who was promoted to the Premier League while on loan at Hull last season, reckons Fulham can still survive if they do not let Saturday's disappointment linger.
"It is important we pick ourselves up now," he added.
"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."
Captain Brede Hangeland has helped stave off relegation in previous seasons at Craven Cottage and feels it is now time for the whole Fulham squad to show what they are made of.
"This is where, as a player, you really show your character and be accountable," the Norway defender said.
"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."
Source : PA