Dunk was at fault for Kai Havertz's opener for the Gunners, before Declan Rice's 49th minute dismissal was followed by Joao Pedro's equaliser for Brighton.
Dunk said afterwards: "I have to look at myself in the first goal.I had to bounce-back from that. In the end, it's a good point the Emirates is a tough place to come."
On his mistake for Havertz's goal affecting him, he continued: "No. Maybe when I was younger. You make mistakes and it's how you react to those mistakes. It was nice to set one up at the other end.
"The way we want to play is forward and vertical - we have quick forwards we can make passes to.
"We didn't create enough chances when they went down to 10 men, but we will go away and look at it.
"We always believe we can win any game of football. We are in a good place and we know we can beat anybody."