The Eagles were 1-0 winners at Selhurst Park, with a goal from the Frenchman sealing all three points for the side.
Alan Pardew’s team are now up to sixth in the table and just a point behind Tottenham in fifth place while they are also not far away from the Champions League places.
They have been in impressive form so far this season, and Cabaye was clearly delighted with the win, saying they are all together as a side.
"It was a tough game but we've done the job," he told BBC Sport.
"We played well and we stayed in a good shape to keep the result. The three points are very good for us.
"It is always difficult when you're 1-0 up and we needed Wayne Hennessey to make some good saves. We stayed strong and solid. We played well as a team. Our mentality is the same - we're all together.”
Given the open nature of the Premier League this season, there is no denying that Crystal Palace will fancy their chances of making Europe.
They are certainly in the hunt for a Europa League place as they sit sixth after sixteen games, but will be eyeing those Champions League places ahead of them.
One big problem for them however is the lack of a proper striker in the squad, with the likes of Cabaye and Yannick Bolasie having been relied upon to score the goals this season.
If manager Alan Pardew can improve that situation in January, it would give them an even better chance of reaching Europe this season.