For me it's very clearly a Southgate problem. When the attacking players receive the Ball in the final third they are dangerous, but they don't get fed enough because Southgate is afraid to sacrifice his more conservative double pivot. Rice in particular is for me extremely conservative with his passing, and has either been instructed not to attempt line-breaking passes, or is not ambitious enough. I'm fine with the double pivot in bigger games, but here when England had 70% possession, I felt Southgate displayed a lack of tactical bravery not changing the shape of his team.
To be fair, it's not fatal. England didn't technically have to win this, and the current system will likely have more success when England can break into space. But I do feel that Southgate isn't quite playing to his player's strengths. This is the most technical England side in decades, and players like Mount, Grealish and For an should be trusted more; their teammates are just not feeding them enough in dangerous areas.