Bobby Zamora's goal cancelled out Ruben Rochina's impressive opener for Rovers, as two of the league's winless teams went head-to-head and drew 1-1.
"I'm extremely disappointed. We dominated completely and should have won. We just lacked a bit of skill and luck," the Norwegian told Sky Sports 1.
"We feel confident here (Craven Cottage) and have had great results here over the years.
"It's too early in the season for us to start looking at the table."
Hangeland missed a fine chance to put his side ahead in the second half and said: "It was a really good chance. I'll lose sleep over that tonight."
The end of the game was soured by a nasty-looking injury suffered by Blackburn striker Junior Hoilett.
The Canadian was knocked out cold following a collision with Fulham keeper Mark Schwarzer as the pair jostled for a high ball.
"He's got three or four stitches in the side of his head and a bang on his eye," manager Steve Kean said of the injury.
"It's not a great challenge and he'll have some concussion. It's a bad one.
"It could have been worse. He was out for a little bit of time and it might affect him for the next game.
"He'll be fine."
Blackburn had lost all three games prior to Sunday's match, and some supporters had voiced their unhappiness with Kean.
He believes the fans will soon be behind him, though, especially if his side play as he felt they did against Fulham.
"We played a lot of good stuff and dealt with the Fulham threat," he said.
"We've got confidence in abundance, we have spirit and togetherness.
"It (the speculation) doesn't affect me, honestly. I have the dressing room and the backing of the owners. If the fans stay with us, we'll see many away performances like that where we win more than one point.
"I'm sure if the fans stay with us we'll finish in the top half."
(reopens) Fulham manager Martin Jol felt his side had missed an opportunity to pick up the three points.
"I felt we deserved more today [Sunday]," he said.
"We are playing at home and we didn't succeed. We know we have to win our home games and we didn't today [Sunday]."