The crowd will largely be made up of children aged under 14 as, under UEFA rules, they are allowed free admission to fixtures played behind closed doors.
“If it is an embarrassment, it is for England as a country,” said the England manager.
“A lot of the people that caused the problems I’m not certain were football fans. We spoke enough about it, we spoke about it after the final and when the punishment was first given.
“What I will say is the vast majority of our fans who travelled to Germany (for this week’s 1-1 draw) behaved brilliantly.
“A big thank you to them because maybe people were thinking something different but there were a huge majority who were a credit.”
England are halfway through a series of four Nations League group fixtures at the end of a draining season.
They were beaten 1-0 in Hungary before drawing 1-1 in Germany on Tuesday thanks to Harry Kane’s late penalty.
Southgate said all of his players were fit but hinted changes were likely against Roberto Mancini’s team.
The Italy manager, whose side failed to qualify for the World Cup, said he was disappointed the teams would not be playing in front of a full house in Wolverhampton.
“We would have preferred to play with supporters,” he said. “Football without supporters is not football and is not good for an important game like this. I agree with him (Southgate).”
He added, “It’s very difficult for me, after one year without supporters (due to the coronavirus), to play again with no supporters, it’s very difficult. It’s better because football is more beautiful with supporters.
“It’s going to be a very different game because we play here and behind closed curtains.”
Italy have drawn with Germany and beaten Hungary this month to top Group A3.
It will be the first time England and Italy have met since the Azzurri came out on top in the Euro 2020 final but Mancini does not believe Southgate’s side are out for revenge.
“I don’t think it’s about revenge. In the future maybe, but not now,” he said.
“This is a different match in the Nations League. For them it’s important to try something new for the World Cup and England will maybe change many players.”