A first-minute strike from West Ham skipper Kevin Nolan was followed by goals from Winston Reid and Matt Taylor to sew up the victory for the Hammers before half-time.
Fulham's defenders were given a torrid afternoon by West Ham debutant Andy Carroll, who was later substituted due to a hamstring injury.
Norway international Hangeland, 31, was hoping to deal with the aerial threat of Carroll but admitted the poor start meant an improved second-half performance counted for nothing.
"We expected to have a lot of possession but we did not defend well enough on the things we knew they were good at, so that is something that needs to improve," he told fulhamfc.com
"It was the worst possible start and we gave ourselves a big mountain to climb; too big.
"We lost the game in the first half and even though we improved in the second half there was too much work to do."
Jol echoed the comments of his captain after seeing his team lose for the third time in a week.
He said: "Normally to analyse a team like Chelsea or Manchester United it is difficult but with West Ham it is easier.
"We know that they will play the long ball and look for knockdowns and the first goal is disappointing because we spoke about it, we did not pick up at the end of the first long ball.
"The second goal was a corner kick and the third goal was the same, a big ball and a knockdown and we didn't pick up the second ball."
Former Tottenham boss Jol also felt his side played better after the interval and reckons his side lacked a recognised playmaker.
"(The second half) was better but we'd almost destroyed ourselves," he said.
"We missed a few players in the creative role behind the striker. That is a worry as we have to find a balance for the future. I think we will be fine."
Jol was quick to praise the impact of new signing Dimitar Berbatov after his introduction as a half-time substitute and Hangeland was also impressed.
"He showed what we knew," he said.
"He is a quality player and we are really happy to have him on board and look forward to him helping us out."
Former Manchester United forward Berbatov was brought in on transfer deadline day as Jol looked to cushion the blow of losing Mousa Dembele and Clint Dempsey in the last week.
Kieran Richardson also moved to Craven Cottage and Jol acknowledged the ex-Sunderland utility man was not match-fit.
He said: "It was not easy for him, he replaced Dembele - a left-footer, he hasn't played a lot of 90-minute games and didn't train for the last three or four days but I think he will be fine in the future.
"I don't think he is a wing player, he is more of a midfielder player or maybe even a number 10 and a left-back. He doesn't want that but I imagine he can play left-back as well."