The 25-year-old was named as Magpies skipper ahead of his side's first Premier League game of the season following promotion from the Championship in 2016-17.
Shortly after the start of the second half, however, Shelvey stood on Dele Alli's ankle after trying to retrieve the ball from him following a stoppage in play, and was shown a straight red card.
Souness, who managed Newcastle between 2004 and 2006, told Sky Sports News: "He's gone from captain to clown in 10 seconds. He's annoyed because Alli has kept the ball. How stupid is that?
"Newcastle are right in the game, he's done it right under the referee's nose, who has no other alternative but to send him off. I was saying... just before it that I liked Shelvey and he has something about him but you can't have anybody doing that at a football club. Nobody.
"He lost them the game arguably. I'm not saying Tottenham wouldn't have won but the game but there would've been a lot more nip and tuck play.
"That should be his last chance because you can't do that. They might get relegated by one or two points. It might not matter in the bigger picture but his teammates have the right to be very angry."
Shelvey has been sent off twice under Rafael Benitez at Newcastle, more than any other player.