Palace twice fought back from a goal down against Liverpool to draw 2-2 in normal time before winning on penalties as Henderson made two saves in the shootout.
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He later told TNT: "These emotions are fantastic. You'd think obviously they were 2-1 up and we were out the game, but the lads stuck by it.
"The manager said we'd get a chance in the second half on transitions, we did. We stuck by it, defended great, and we deserved that in the end."
Henderson also said: "I love it, I love the big moments, I love being in that pressure moment. I really enjoyed that today, the homework we did for the penalties was great, so thanks to everyone behind the scenes that helped me with that."