The Premier League champions looked set for a comfortable win against 10-man Newcastle after goals from Ryan Gravenberch and Hugo Ekitike either side of Anthony Gordon's red card.
But Newcastle came roaring back at a raucous St James' Park and looked to have snatched a point after goals from inspirational captain Bruno Guimaraes and an 88th minute leveller from substitute Will Osula, only for 16-year-old Rio Ngumoha to hit a 100th minute winner for the visitors.
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Slot said: "I've experienced a game like this once before since I came to England, that was Everton away last season, where so many things happened, where it was complete chaos, where the fans were so there for the whole team and our fans tried to help us as much as they could.
"It was an unbelievable atmosphere and for us to stay strong in that atmosphere for such a long time is worth more to me than when we win 4-0 or 5-0..
"For me, tonight had nothing to do with tactics or good football.
"The best part for me of our game, after we conceded for 2-2, was also their best part of the game. They got three or four corners, 15 throw ins, 112 free-kicks...it felt so much.
"We had to defend so much. They were so close to scoring but we stood strong.
"Then at last after four or five minutes, we got the ball. It's of course special for Rio to score a goal in a moment like this.
"We know how it feels, last season we conceded in the 89th minute here, now we were the lucky ones. We were lucky to get over the line."
Slot said he was "not at all" disappointed about the manner in which his side lost control in the second half, despite having a man advantage after Gordon's red card, and instead praised Newcastle.
He said: "That's what their playing style brought.
"You can't control a game of football when every single ball is thrown into the box, every throw is long, every free-kick is a long ball. They can do both, that's why they're such a good team.
"They can play out from the back if they want to, they can be intense in their pressing, they have so many quality players.
"But they also have the quality to play a game like this. You cannot control a game of football like this."