Looking back over the 90 minutes, Cahill said: "I thought we were in the game, to be honest with you. When we were level at 1-1 we had a couple of chances after that to go ahead. Disappointing for us today.
"We tried, we tried to create and we had big spells in the game I thought. I did think the scoreline flattered them but, having said that, defensively the goals were disappointing, the goals were sloppy and we’re not normally like that. That was not good enough defensively for a couple of incidents.
"I was disappointed in the second one. Such is life. We have to keep going and push on. We felt that last week we played very well and didn’t get the result. This week we were well in the game and we lost again. We need to take this period now, we need to rest up and we need to come back fighting for the last part of the season."
The squad now have 13 days without a game as the second half of the Premier League enters its winter break. Cahill looked ahead at the coming months and expressed his view for the Eagles' best approach.
"It’s down to us to change it," he said. "We have to work together to change it. We know we’ve got enough in there, we’ve played well enough this season to know that we can kick on in the league.
"We had decent results against Arsenal and [Manchester] City and then the last three have been very disappointing. We need to switch back on to winning ways and recharge mentally and physically to come back stronger."
You can watch full post-match reaction as well as highlights via Palace TV. Head there now by clicking here or 'Palace TV' within the official app.