"We were able to get more pressure higher up the pitch, we were able to get tighter to their midfielder".
Mandzukic retired from worldwide duty following his country's run to the World Cup final and Croatia have scored just one goal in three matches since, the latest of which was a 0-0 draw against England on Friday.
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".
Follow the Football match between Croatia and England live with Eurosport. "The most important thing for the team is we create chances, look unsafe, and the players who didn't score tonight will score".
"We don't want to overburden players. The second-half performance was excellent, we were pushing and pushing right to the end and on another day we would finish those chances".
"We could easily hear the ones on the hill", said Dier.
It was a surreal and unusual experience watching the Three Lions with atmosphere replaced by silence and the World Cup semi-final rematch suffered as a result.
Dier headed Jordan Henderson's corner off the post a minute before the break.
Kane headed a Henderson free kick against the bar before Manchester United forward Rashford served up a pair of astonishing misses in the space of two minutes.
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. Several young players were called up for the Three Lions' upcoming stretch, including 18-year-old Jadon Sancho, who's the first player born this millenium to be selected to the English senior team.
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 worldwide debut before the match fizzled out in the final few minutes.