The Three Lions mustered just one shot on target in the 0-0 draw with Harry Kane failing to make an impact and home fans made their feelings clear at full-time by booing Gareth Southgate's side off.
Scotland great Souness was beaming at his nation's display but was not so kind to England, as he warned they won't achieve anything in his tournament unless they can somehow get talisman Kane firing again.
"Harry is England's one player proven to get goals at this level on a regular basis. If that is not happening in this competition, you're not going very far," he said.
"Go back to the World Cup in Russia, his goals got you where you got to and Harry Kane not performing is a major problem for you.
"Football ain't coming home with that, not the way they are playing."
Ian Wright also questioned some of the decisions made by Southgate on the night.
The England legend couldn't understand why Phil Foden was taken off and Jadon Sancho left on the bench.
Speaking alongside Souness on ITV, he said: "The substitutions confuse me. I don't know what to think with that.
"What's he take Foden off for? There is no way Phil Foden should be leaving the pitch today, for me. It's very disappointing to see.
"You have someone like Jadon Sancho on the bench, 16 goals and 20 assists this season, and he doesn't even get on when we need to create.
"We can talk about Harry Kane and the chances he could have had or the touches he hasn't had, but did we really create enough? We're meant to be favourites to win this tournament and I was embarrassed for us today."
Kane has not had a shot on target in the first two games of Euro 2020 and Roy Keane believes Southgate did the right thing in taking him off.
He said: "He does look leggy. He doesn't look up to speed. He's on his heels all the time. If England really want to compete in this competition, you need your star men to perform.
"We've seen Romelu Lukaku turn up, Kevin De Bruyne, Cristiano Ronaldo - they need Kane at his best.
"I'm glad Gareth took him off as there's all this talk about him being undroppable and he's the star man - if he's not performing you get him off.
"Rashford gave them a bit more energy, but still not enough."
Souness added: "The centre-backs had an easy night against him. Harry Kane was a shadow of the player we know he is.
"In two games, he looks leggy, lacking in enthusiasm. A centre-forward is 90 per cent relying on passes and he's not getting a great deal from his midfield.
"I don't care what anyone is saying. That ain't working."