"We still changed the history of the past 28 years. We have had a fantastic journey, further than we thought", he added. But the team will be stronger for it.
Speaking on the eve of Croatia's meeting with England, Dalic said: "We are a country where anything is possible, so there are no surprises". That's what we aimed to do in the long-term.
"We've proved to ourselves that is possible and we've proved to our country that is possible".
"Now we have a new benchmark, a new level of expectation, a new scenario".
The 51-year-old made it his mission to change that and the results have been spectacular, most notably a 3-0 demolition of Argentina in the group stage, although the side has needed penalties to get past Denmark and hosts Russian Federation in the knockout stages.
"If I was in charge of the FA there would be no doubt that I would keep Gareth Southgate and Steve Holland in their jobs and give them the chance to take the team to the next Euros and the next World Cup". "Why didn't you ask me about when I played well against him?"
"1998 will never be forgotten and should not be, but I would love it if eventually the 1998 "Fiery Ones" can be moved aside so that we can talk not only about 1998 but also a bit about 2018", the former Real Madrid player said. You don't get that reaction if you haven't played as well as you have.
But as he conducted his pre-match press conference, football was not the only topic after cameras had captured the players throwing a rubber chicken to each other during their warm-up. "It has a slightly different feel for me, but it's nice to hear people enjoying it again". We should be proud of that.
A huge Croatian flag was unfurled in Moscow's Red Square in the hours leading up to kick-off, while one fan told CNN's Antonio Mortensen that 15 extra planes had been chartered to fly fans out for the match. "I'll go even if England don't make it, the atmosphere will be great".
"Croatia are an excellent team with some outstanding players", he said.
"There's an very bad lot of people with their heads down but they should have their heads up".
"We managed to get through that and regain our composure".
"It's not their first tournament, it's maybe the last World Cup for a couple of them, but I think maybe now is the right moment". The 26-years-old went off during the seventh minute of their extra-time.