Hornets midfielder Chalobah had to settle for a watching brief from the bench in Rijeka but Borussia Dortmund winger Jadon Sancho, who left Vicarage Road for Manchester City in 2014, became the second youngest England player to win his first cap in a competitive game behind the legendary Duncan Edwards when he replaced Raheem Sterling in the 78th minute.
Three Lions captain Kane, 25, has only scored six times in 16 games for club and country since netting that many in three World Cup matches in the summer.
Croatia were completing a UEFA sanction to play two games behind closed doors after a swastika symbol was carved into the pitch during a Euro 2016 qualifier against Italy in June 2015.
Eric Dier also hit the post and he only had words of praise for Sancho after the game.
England's Jadon Sancho, Borussia Dortmund's exciting 18-year old winger, produced a darting run late on after coming off the bench to replace Raheem Sterling and make his global debut before the match fizzled out in the final few minutes. That approach earned Mateo Kovacic and Dejan Lovren bookings.
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Southgate can take some comfort, however, in the fact England adapted to these unusual surroundings better than Croatia and created by far the better opportunities. Andrej Kramaric had the hosts' best chance, but placed his shot from Ivan Perisic's cut-back too close to Jordan Pickford, who made a smart save.
In front of the empty stands, Marcus Rashford missed two glorious chances to exact England a small measure of revenge for missing out on the World Cup final to Croatia 93 days ago in Moscow.
"It was a tough evening against Croatia and a weird game to be involved in with no fans - but we coped well".
The 24-year-old produced occasional flashes, especially when driving into the area amid penalty claims when he tangled with Ante Rebic - but too often his game was loose in possession and, perhaps understandably, he looked nervous.
Kramaric sliced wide before Croatia made the night's first change, Perisic making way for Marko Pjaca and the substitute nearly making an instant impact with an effort that curled wide.
Kane believes the performance against Croatia in Rijeka and the narrow defeat by Spain at Wembley last month is clear evidence that this England side are making progress.
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