Liverpool pressed for a winner but Dann headed in from a corner in the 82nd minute to catapult Palace into eighth place on 19 points, two more than Liverpool in 10th.
"I had a feeling that I was going to score and thankfully it was the winner," the Liverpool-born Dann said.
"I have always dreamed of scoring here so it's a nice touch. I'll probably get a bit of stick from my family and friends but they support me as well so I'm sure they won't mind too much."
The loss left Liverpool's German manager hoping his side would finally learn their lesson after conceding late for the second time in three Premier League games since he took charge.
Liverpool drew their first game under the German 1-1 against Southampton when Sadio Mane struck in the 86th minute to cancel out Christian Benteke's opener 13 minutes from time.
"It's not a problem to lose a game, that's football and it happens all the time," Klopp said after Sunday's defeat.
"But we have to learn the right things and if we learn the right things tonight, then it was very important that we lost tonight and good that we lost tonight.
"We have to learn that we decide how strong we are, we decide how good we are, we decide how awake we are, we decide how tired we are -- nobody else.
"We decide when it's over... between 82 and 94 minutes, you could make eight goals if you want and we have to work for that.
"The big decisions are made in the moments when you are tired... It's always when you are under stress. That is everything we can learn," he added.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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