Arbeloa and his Fulham side are still looking for their first Premier League point, currently sitting down in 19th after their first three games.
Fulham took an early lead against Palace through young Josh King, only to be pegged back by Tyrick Mitchell just after the half hour mark.
New summer signing Cesar Palacios then restored their lead going into half time.
Palace came out of the break swinging. Mitchell got his second goal of the game in the 54th minute, while Ben Chillwell signed off his return to the club with a 77th minute winner.
Speaking to BBC Match of the Day after the game, Arbeloa praised his players, and insisted the defeat was harsh.
"I think we didn't deserve to lose this game. I think my players did everything, good attitude, they were brave, so many chances to score more goals," he said.
"They (Palace) took their chances, in the end football is about that.
"We were really unlucky in this goal (second Palace goal), we had many chances also we were very unlucky. Good effort from Gonzalo, that's the spirit I want from my players, the striker making a sprint to try and save a goal. With that spirit and character, if we play in this way, the victories will come.
"We did many good things to win the game, it was similar against Chelsea but we lose. For the players it's a difficult situation, difficult moment, but I am very proud of them.
"Cesar Palacios and Gonzalo Garcia both had a great game, Cesar scored a goal, and for Gonzalo another great performance."