The Blues left it late before Seamus Coleman smashed in the winner before celebrating in front of the Everton fans, something which pleased Koeman.
Koeman said that after the win over Manchester City, everyone expects another terrific performance, and while this was a different type of game, the win pleases him.
“It was deserved,” he said.
“It’s not bad to score a late one because it doesn’t leave Palace long to equalise.
“We played really well. We had a lot of shots on target but their goalkeeper played really well.
“The whole team did well. After City, everyone expects the same performance.
“But this was a very different game. I’m pleased with the win.”