Zaha's goals mean Palace will play Watford in the final at Wembley and the Manchester United-bound youngster found it hard to describe his feelings.
He told Sky Sports: "I can't explain it. No words can express how I feel.
"I have played for Palace for ten years. I am just happy I scored and finished strong for the club.
"We go to Wembley now and that's a dream"
Julian Speroni starred in the Palace goal and played down his part in the victory.
He said: "I just do my job and I am pleased I helped the team go through."