"The atmosphere is not easy for anybody. It is sad for football but hopefully this is our last time," said Dalic.
"Football is played for the fans. It's sad the second and fourth team from the World Cup are playing behind closed doors. I don't know who it is good for."
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.
"We dictated the flow of the game for a long period. The second-half performance was excellent, we were pushing and pushing right to the end and on another day we would finish those chances."
A small band of England supporters perched on a hill overlooking the deserted 8,000 capacity stadium in Rijeka tried to offer their encouragement.
However, a point does little for either side's hopes of usurping Spain, who beat both last month, to progress to the first ever Nations League semi-finals next summer.
"We could easily hear the ones on the hill," said Dier. "They were the only ones here."
- England rue Rashford chances -
Mario Mandzukic scored the winning goal to end England's World Cup dream in Moscow, but without the Juventus striker, who has since retired from international football, Croatia lacked a focal point up front.
"We need to stop talking about Mario Mandzukic," added Dalic.
"He is not here and we need to respect his decision."
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.
England's prowess from set-pieces played a huge role in their World Cup success and again proved a potent weapon.
Dier headed Jordan Henderson's corner off the post a minute before the break.
And six minutes after the break Kane rose highest to a Henderson free-kick only to see his looping header come back off the crossbar.
Dalic complained after a 6-0 thrashing at the hands of Spain that his side were still fatigued from their summer exertions and they faded again as England took control at the start of the second period.
Ross Barkley had strong claims for a penalty waived away on his first international appearance for two-and-a-half years before Rashford was twice presented with golden chances to score for the third straight game for his country.
But on both occasions the Manchester United forward produced weak finishes to Dominik Livakovic's left-hand side and the Dinamo Zagreb goalkeeper made comfortable saves.
"On another day we would have won 3-0," said Barkley.
"We should have been more ruthless."
Southgate threw on 18-year-old Jadon Sancho for his international debut 12 minutes from time in search of a winner.
The Borussia Dortmund wonder kid showed some impressive touches but couldn't provide a final spark as England had to settle for a point.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)