Croatia looked on course for a place in the last 16 after Ivan Perisic gave them the lead early in the second half.
However, Portugal fought back through Cristiano Ronaldo and Goncalo Ramos to complete the comeback and secure their place in the next round.
The Croatians thought they had forced extra time when substitute Josko Gvardiol found the net in the closing moments, but the goal was ruled out following a VAR review for offside in the build-up.
Dalic made it clear he was frustrated by the decision but chose not to criticise the officials directly.
"Please don't have me speak about the disallowed goal," Dalic said. "I've already said what I think and I don't want to go into deeper analysis.
"These decisions take away the joy of football. I'm not saying VAR cannot help, but it kills the emotions. Football should be fair, but I think we've gone too far with VAR. Croatia lost the match, we are disappointed and I congratulate Portugal, but I don't want to discuss it further."
The Croatia coach also reflected on the late winner that ended his team's hopes.
"It is never easy to concede in the last minute. We should have dealt with the situation better. We also needed to be stronger in the first half because we created good chances. It was a dramatic match full of emotion, but that is football."
Dalic reserved special praise for captain Modric, who is widely expected to have played his final World Cup match. He has played in five FIFA World Cups for Croatia.
"This was probably his last World Cup and I am sorry it ended with a defeat," Dalic said. "Luka came on in the second half and once again showed his quality and character. He led Croatia until the very end, and I feel sorry that his World Cup journey finished this way."
The Croatia manager also thanked the supporters who backed his team throughout the match.
"Our fans gave us incredible support. It was a wonderful football atmosphere and I hope football always keeps that spirit instead of becoming only a business."
Julian Nagelsmann has resigned as Germany head coach following the national team's shock World Cup exit to Paraguay, the country's football federation confirmed.
Jurgen Klopp has emerged as the leading candidate to replace Julian Nagelsmann as Germany head coach, but the German Football Association could face difficult negotiations with Red Bull before any appointment is completed.
Argentina coach Lionel Scaloni has said his side will not underestimate Cape Verde when the reigning world champions face the tournament debutants in the 2026 FIFA World Cup Round of 32 on Friday.
Ghana head coach Carlos Queiroz believes there will be little margin for error when his side takes on Colombia in the FIFA World Cup 2026 Round of 32 on Friday.
