Manuel Lanzini scored the only goal of the game at Selhurst Park as the Hammers brought a five-match winless run in the Premier League to an end.
West Ham had to dig in as Aaron Cresswell was controversially sent off for two bookable offences with 15 minutes remaining, and Noble was delighted with his side's attitude as they picked up a first league victory since August.
“I thought we were tremendous,” Noble told the Evening Standard. “They’ve got big players like Connor Wickham and Christian Benteke up front, but I thought our defence did a magnificent job, they dealt with them incredibly, it’s a top, top win for us.
“I said in an interview the other day that everyone here really does care, and I think we showed that.
“We looked at how Palace play and everything goes through Benteke so we knew we had to deal with that threat. Cheik [Cheikhou Kouyate] is great in the air, then alongside Reidy [Winston Reid] and Angelo [Ogbonna], obviously Cress [Aaron Cresswell] back in the side, we played like a proper team.”