Matt Spring's early strike gave the Addicks three precious points to end a club record run of 18 games without a win.
Parkinson believes that the battle shown by his players at The Valley can be taken into this weekend's trip to Burnley and hopefully for the rest of the season.
"It was a terrific performance in terms of resilience, desire and commitment, and that's what won the game in the end for us. We knew what we'd have to deal with and Palace had a real go at us; it was a proper derby. But we stood up to it", said Parky.
"People who've seen us at home recently will know we've played well at times and we've been close to winning. There's no better example than the Derby County game when we conceded with the last kick of the match.
"The longer you go without a win, the harder it becomes. But we told the boys on Monday that they've got an 18-game road to survival and we told them what they needed to do to get to the point of survival, and tonight is the first step on that road.
The former Colchester boss added, "It means a hell of a lot to me. When you're a manager and you haven't got that win, then it's tough. You just have to keep believing in what you're doing and keep doing what you're doing and hopefully the victory comes. I'm pleased for myself and for all my staff, who have absolutely worked their socks off. Their effort has been first class."