Fernandes says the focus must now be on their Europa League campaign.
The captain said afterwards: "I think we controlled the game. In one moment in the first half where we concede the goal, we talk about during the week, that they do that in set-pieces. We should have been more aware of that.
"But I think we controlled the game in the first half very well, we had some chances, in the second half even more.
"Then in extra-time, I think Fulham had a little bit more control of the game, but we had the better chances to end up scoring a goal, but we didn’t, and then the penalties, they were more efficient than us."
Fernandes agreed when it was put to him that our fighting spirit is still strong but, ultimately, felt the special moment needed for us to get a winner did not come.
"I think it’s (fighting spirit) always been there but, obviously in (some) moments, you get goals. In others, you don’t. Against Everton, it wasn’t enough to get the win. Against Ipswich, it was. Today was enough to get us into extra-time and then into penalties but, as I said, they were more efficient than us.
"Unluckily for us, it’s a dream that getting into the final at Wembley again that is not there anymore, but we need to keep pushing for what’s left of the season."
Looking to their Europa League round 16 tie with Real Sociedad, Fernandes said: "We know that we had many injuries in this period and we don’t have as many players and we’ve been playing almost always with the same players for long spells, it’s been difficult.
"We just now need to recover, focus ourselves to the best we can to get (to our) best, fresh legs to the next games.
"It’s going to be a tough one, a Spanish team that plays brilliant football, very, very good players up front, very (high) quality coming out from the back, so we need to be fresh to run again because they will make us run, and then when we have the ball, we have to make them run, too."