Arsenal were dominant in possession and created more of the chances but it was yet another inefficient performance from the North Londoners which left manager Wenger a dejected soul.
"I'm very, very disappointed," Wenger added.
"You have to sometimes win 1-0 and this was one of these days.
"We had 70 per cent time with the ball and we didn't make enough of it.
"We lacked accuracy in our final ball and change of pace, didn't play with enough freedom and flow.
"In the end we got caught with basically a unique shot on goal from Crystal Palace. They played deep, they defended well and they got us on the break.
"That's the story of the game, even if it's very frustrating."
He added: "We gave a goal away that was avoidable. That's the regret of the day."
Arsenal now sit fourth on the Premier League table, 13 points off league leaders Leicester City, five behind second-placed Tottenham and equal with Manchester City in third but behind on goal difference.