Campbell admitted he and the players had looked at Palace's history at Everton, while he thanked the fans for being patient with him.
"I am delighted to score but also to come to a difficult place and get three points," he told the Croydon Advertiser.
"We looked at Palace's previous results at Everton and we've got a great track record.
"The lads showed why - we got stuck in and stuck to our guns and everyone worked hard to get the result.
"Everton, with their last couple of results, they have done really well. It was important we calmed them down and managed to score.
"The lads' character came back into the game and won it. We chased down a lost cause today and James (McArthur) managed to get in front of the keeper."
For the big stories and the banter follow us on Twitter: @tribalfootball