Ante Rebic pounced on a goalkeeping error from Willy Caballero to put Croatia ahead, before Luka Modric and Ivan Rakitic netted in the latter stages of the game to top off a perfect night for their country.
Dalic is determined to enjoy the historic moment with his side, but insists that staying humble is important to progress further in the competition.
"I have trusted my team from the first day. I didn't believe we would be through after the second game. Argentina were not confused we were excellent," Dalic told reporters after the game.
"We have to be happy because we have done a lot of good things. We have emerged from the group after two games and we have beaten a strong Argentinian side with the best player in the world. But we have to be calm, humble and dignified. We have to be disciplined and I want my 22nd player to be as hungry as my first player to achieve victory.
"Every coach has their own style of work. Over the last few days we haven't looked at tactics because I wanted to relieve my players of the stress. I recently said this was going to be our best match because we played with fluidity and confidence and the whole of Croatia enjoyed it."
Croatia are five points clear at the top of Group D, with Iceland being their only remaining fixture of the group stages.