With the score locked at 1-1 at the final whistle, the tie went into a penalty shootout which saw Benitez save twice on his Palace debut as the hosts won on Tuesday night.
Benitez told Sky Sports: “It's difficult when you play in a derby – it's always like a fight.
“We played a good game, and I think we created the most chances to score. But we are happy with this qualification, and now we think about the next round.
“It’s my first game with Crystal Palace, and I'm very happy because I don't play after a long time. And for me, this one is like one gift, so I only enjoy this game. I know it's special for the fans because it's a derby, and so we are happy with this result.”
Palace No1 Dean Henderson entered the pitch after Benitez's heroics and celebrated with his fellow goalkeeper.
Benitez also said, "We are together. We are one team.
“And, you know, he stopped a lot of penalties for Crystal Palace, so we work together in this case, and I'm happy with this also, because we talked about this before the game and now we have the big result – so I'm very happy."