Adrian Mariappa had given Palace an early lead before Kasami controlled Sascha Riether's pass on his chest before volleying a superb shot beyond Julian Speroni to draw Fulham level.
Steve Sidwell struck another excellent volley for Fulham before second-half goals from Dimitar Berbatov and Philippe Senderos made sure of the points.
"No, to be honest," Kasami told Sky Sports when asked if he had scored a better goal.
"I'm very pleased that we won that game as we were losing 1-0. Thanks to Sascha for the great ball and it was an unbelievable goal. I'm very pleased.
"I saw Sascha had the ball and saw I could run in the space. It came perfect to my chest and I took it direct with my right foot."
Fulham had beaten Stoke at home prior to the international break and Kasami added: "I'm very pleased for these two great wins. It gives us a lot of confidence if we keep playing like that and we can improve."
Fulham boss Martin Jol has reportedly been under pressure in recent weeks and Sidwell was pleased to contribute to a third Premier League win of the season.
The midfielder said: "Obviously, we've all been under pressure and not just him. We put ourselves under pressure to perform week in, week out.
"We've been disappointed with the results we've taken so far, especially letting in silly goals as well.
"Hopefully now we've got back-to-back wins, it puts a lot of spirit in the camp and takes a bit of pressure off us and the boss himself, and we can go out and play our football."