Croatia were punished after a swastika was marked on their pitch before a Euro 2016 home qualifier against Italy.
“It is a shame for the travelling fans and those who have not missed a game for decades,” Southgate said.
England are aiming to avenge defeat by their hosts in the World Cup semi-final just 93 days ago.
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Southgate said: “We do it every day of our lives – playing football in front of a handful of people watching – so it’s not totally unique, but in a match situation it’s different.
“I’m sure Croatia feel the same. They’d like to have the encouragement of an incredibly passionate support.”
The crowd will be officially registered as zero but there are likely to be about 500 people in the stadium, with about 150 media expected and a maximum of 75 people per team delegation, including the players.
There will be a maximum of 200 people holding top-category tickets from the visiting association as well as police officers, security staff and people carrying out functions relating to the stadium infrastructure.
There will also be a maximum of 75 Uefa representatives, as well as Uefa partners holding complimentary VIP tickets.
Southgate said: “It means Croatia don’t get the energy the home support can give you in those moments when you’re under pressure. Whether it’s an advantage, though, who knows?”
This is not experimental – Southgate
Croatia manager Zlatko Dalic has already named his starting XI for the match, with Luka Modric and Ivan Rakitic among six players included who started the semi-final victory over England in Moscow.
England have lost Manchester United left-back Luke Shaw to injury, while Southampton goalkeeper Alex McCarthy, Spurs full-back Danny Rose and Arsenal striker Danny Welbeck have also returned to their clubs.
Southgate’s squad has a youthful look with the inclusion of teenagers such as Borussia Dortmund’s Jadon Sancho and Chelsea’s Mason Mount, who is on loan at Derby County, plus Leicester City’s 21-year-midfielder James Maddison.
But he insists this is a squad picked to win this game, and the other Uefa Nations League match in this double-header – against Spain in Seville on Monday.
He said: “We’re here to get a result. It is not experimentation. It is players we believe in. The team who play will be the team we believe in. There’s no-one in the squad here who we wouldn’t put in the team.
“Some are relatively inexperienced at the highest level but they’re people we’ve enjoyed working with and have shown they can handle themselves at this level in training this week.”
Croatia’s starting XI: Livakovic, Jedvaj, Lovren, Vida, Pivaric, Rakitic, Kovacic, Kramaric, Modric, Perisic, Rebic.