Meanwhile, Croatia will face England in the second semi-final in Moscow on Wednesday.
Croatia are just the second team to win successive shootouts in World Cup history, emulating Argentina's feat in 1990, when the latter won shootouts against Yugoslavia and Italy in the quarters and the semis, respectively.
"We're grateful for the emotions, our hearts are broken, but thank you to everyone who supported us...", he said, before breaking off the interview. Both Russia and Croatia had needed extra-time in their matches against Spain and Denmark, respectively, and thus emulated South Korea and Spain, who needed extra time and penalties to separate each other in the last eight of 2002.
Kane is leading the Golden Boot race with six goals and is one short of eclipsing Gary Lineker as England's highest ever scorer at a World Cup.
Dalic blamed Croatia's opponents for smothering the creative talents of Luka Modric and said he expected a more open match in Moscow's Luzhniki Stadium.
"That defeat is completely irrelevant", he said, with a face like thunder.
Modric has scored twice in Russian Federation, including a fabulous goal in the 3-0 win over Argentina in the group stage, and twice netted in nail-biting penalty shootouts against Denmark and Russian Federation.
That caution is disappointing but if there is a silver lining for Dalic, it is that his team once again showed the mental strength to win on penalties - a not inconsiderable feat in front of a partisan 44,000 crowd in Sochi.
Now they are looking to go one step further, but just getting this far is a source of great pride for Croatia.
He went on to further praise Sterling's "pace and power" and said his coaches would be analysing Gareth Southgate's team closely over the next two days. The hosts lost 4-3 in the penalty shootout.
"We watched England and we saw how strong they are", Modric said in the post match press conference after his sides quarter-final victory.
"He has minor issues but we have a huge game tomorrow". We have played five games, but being exhausted can not be an alibi.