Arsenal have conceded only three goals this season and come into the match against Palace off the back of a remarkable 4-0 win over Atletico Madrid.
Meanwhile, Oliver Glasner’s side were on the end of a Conference League humbling on Thursday night, falling to a 1-0 defeat against AEK Larnaca, who are fifth in the Cypriot League.
Palace’s shock loss was just their second of the season, and they will attempt to bounce back at the Emirates with their first of three games in six days.
Victory against red-hot favourites Arsenal could catapult Palace into the top six, and Henderson reckons they should go into the game with nothing to lose.
“The reality is, you go to the Emirates and it's a free hit,” said Henderson.
“We've got to go there, play with confidence, enjoy playing there and see what we can do to cause an upset.
“We have to use it as a cup game, a one-off game and the pressure is on them. We will go there and do the best we can.
“It would be great if we went there and won. It would change everything. We look forward to it. It’s a free hit.
“We'll give it our best shot. We've delivered against teams like that before, so why not do it again?”
Palace have faltered in front of goal this season, underperforming their expected goals by 7.10 – the most of any team in the Premier League.
However, Henderson, who has a front row seat for Palace’s missed chances, says it would be more troubling if they were not creating opportunities rather than lacking the finishing touch.
“Once the goals start going in, we will be scoring six or seven a game. We’re scoring enough goals.
"But we have to keep them out as well, which we did so well at the start of the season, but not of late.
“We’ve got to keep going, work hard on the training pitch, stick together and everything will be good.
“The positive thing is that we are getting chances. When I arrived at the football club, we didn’t create many chances, maybe one or two.
“Now we’re creating six, seven big chances a game. When they start going in, it will be fantastic.
“We have a good group of players and a fantastic manager – it’s not something we dwell on. The missed chances will start going in soon.”