The Eagles started the game on an impressive note with Luka Milivojevic converting from the penalty spot after Cheikhou Kouyate was fouled in the box.
However, the Gunners fought back with Granit Xhaka levelling proceedings before Pierre-Emerick Aubameyang scored the second for his side but another Milivojevic’s spot-kick helped Roy Hodgson’s men avoid defeat in front of their home fans.
And the 20-year-old who featured for the entire duration of the encounter has praised the team’s fighting spirit.
"We started well, we created a lot of chances and we took those chances. Then, second half they got back into the game but we kept fighting to the end,” Wan-Bissaka told club website.
"The team has got confidence, especially going forward, and that helps against a team like Arsenal."
On Milivojevic’s goals, he said: “I was confident that he was going to score, so well done to Luke for getting the two [goals]."
The wingback has helped Palace keep three clean sheets in nine league appearances this season and he wants to continue with the form.
"I want to keep on doing what I'm doing. Arsenal are always a challenge but challenges help me. The fans are all good to us, they're behind us and carry us all the way."
Wan-Bissaka will now shift his attention to the League Cup when Crystal Palace travel to Riverside Stadium to take on Middlesbrough on Wednesday.