No Croatia player played more passes in the opposition half or sent in more crosses than the Real Madrid midfielder, and he drew a save from Pickford with a fizzed shot from distance in the second half.
The virtually-empty Stadion HNK Rijeka hosted England's first-ever match behind closed doors as Croatia completed a ground ban imposed by UEFA for having a swastika on the pitch during a Euro 2016 qualifier against Italy.
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".
Failure to win this match means England need three points from their clash with Spain in Seville on Monday evening (Tuesday morning AEDT) to stand any chance of winning Group Four, as both sides sit five points adrift of Luis Enrique's men.
"We could easily hear the ones on the hill", said Dier.
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A Red Star Belgrade spokesman, Nebojsa Todorovic, told AFP: "I can not comment on this in any way". Dzajic added that he knows "absolutely nothing about this - it is not possible, it is untrue".
The game was built up by some English media as a chance for the visitors to avenge Croatia's 2-1 World Cup semi-final win in Russian Federation in July but the game failed to produce any fireworks. "But we have to forget Mandzukic, it is over, he is not with us anymore".
That result followed a 6-0 drubbing at the hands of Spain but coach Dalic is focusing on the future, rather than dwelling on the past.
"He made his decision and we have to respect that and look for other solutions".
England still have three other goalkeepers to choose from but Rose's exit, which came after Luke Shaw was forced to leave, means that Leicester's Ben Chilwell is now the only left-back in the squad.
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.