The Cottagers came within 10 minutes of being dumped out of the competition on their own patch on Saturday but Giorgos Karagounis' sensational equaliser denied the Championship club a famous win.
Stockdale, who avoided a repeat of his horror show in his last home game against Swansea, said: "We were going for it a bit more so we got caught a few times. We might have been more patient, but I'm confident going up there as well.
"They will fancy their chances up there but we have to play the same way with the same attitude. I think the goals will then come."
Stockdale insists Fulham should have sealed a place in the fourth round at the first time of asking.
The 27-year-old said: "We dominated the game but a silly bit of defending cost us. We had a enough crosses and chances to get more out of it.
"It wasn't to be be but we have to keep the faith. Blackpool was never going to be walkover."