Eric Dier and Harry Kane headed against the woodwork for the visitors while Marcus Rashford spurned two clear opportunities as England missed out on a first win in the new competition.
The result inside the near-deserted stadium left both sides with one point from two games behind runaway leaders Spain, who have six points and host England in Seville on Monday.
England manager Gareth Southgate was disappointed with the outcome, saying: “Second half we were by far the better team and if we had taken our chances we would have won the game.
“There would be more concern if we were not creating chances. We showed good endeavour and creative play. We have to keep getting in those situations.”
Without any fans present as Croatia served the second game of a crowd ban for racist offences by their fans in Euro 2016 qualifying, the instructions from both benches echoed around the eerily empty ground in a tepid first half at the Rijeka stadium.
Midfielder Dier reflected on the first match England had ever played behind closed doors, although he noted the presence of a handful of England fans on a hill overlooking the ground.
“It was strange, the first experience of it for all of us,” Dier told Sky Sports. “A couple of fans got up on the hill but once the game started it was in the back of our minds. We could easily hear the ones on the hill, they were the only ones here.”