Palace defeated Fulham on Saturday to reach the final four, where they will meet Aston Villa.
"It’s unbelievable,” the England international told Palace TV. “Obviously, we know how big this game was for the supporters as well as the players.
“We rode a storm for the first 20 minutes, and got a foothold in the game with a bit of brilliance (from Ebere Eze). The boys were unbelievable, they ran themselves into the ground.
“A lot of lads got back in late as well this week (from international duty) and it took us probably 20 minutes to click as a team. To a man, (we were) unbelievable.
“We’ll just keep going, keep rolling with the punches and keep enjoying it.”
Henderson also said: “They (the fans) were the 12th man today. Obviously, they helped us get through the first 20 minutes – and if Fulham get something in the first 20 minutes, it's a different game. They were always there with us.
“It can happen in a flick of a switch. If you concede a goal, 2-1, it changes the whole complexion of the game.
“So the boys at the back were phenomenal. They're talking to each other, communication, just helping each other out. And we've seen off all the threats and it's been a great day.
“As I say, the boys were phenomenal and they're putting a right shift today. Obviously, we're all delighted and we're just excited for the next round.”