Andrej Kramaric's opener in Sunday's decisive meeting at Wembley looked set to give the World Cup finalists another victory over the Three Lions.
But Harry Kane's effort ran for Jesse Lingard to equalise before the hosts' captain converted a Ben Chilwell cross in the 85th minute to instead book England's place in the Finals.
Speaking after the game, Dalic was quick to praise his opponent saying: "First of all congratulations to England on a deserved win and qualifying for the final four. We didn't play well in the first half and we were a bit lucky to get in at 0-0, but the second half was better.
"We had a few chances after scoring but conceded two set pieces and in the end it's fair as they are a part of the game and a fair result. I'm not a sad man, I'm proud and we played well, I congratulated them on their performance.
"I think England showed already at the World Cup they exceeded expectations. They have a really young and very fast team which is important in modern football."
Dalic even joked: "It’s coming home, very soon," in reference to the England anthem 'Three Lions', which enraged some Croatia players over the summer as they felt it disrespected their side in the build-up to their World Cup semi-final meeting.
Croatia were without key midfielder Ivan Rakitic due to injury and had to replace right-back Sime Vrsaljko, who made a brilliant tackle to deny Marcus Rashford, in the first half at Wembley.
Ante Rebic was also withdrawn at the break, while England could introduce Lingard, Dele Alli and Jadon Sancho, and Dalic said his stretched squad lacked energy following their exertions in securing a last-gasp 3-2 win against Spain on Thursday.
"[Conditioning] was our biggest problem as you saw with Sime Vrsaljko and Ante Rebic, it was very difficult to recover from the match against Spain," he added. "We don't have a big roster of players and missing five players means we can't just replace them.
"In the second half England were not very dangerous, we played well but we lacked concentration in the last 15 minutes which can be taken from our condition physically.
"We didn't have many solutions on the bench, look at who came in for England - they had two players worth €100million and we had two Under-21s and we'd already made two substitutions so we didn't have a lot of options."
Despite their Nations League disappointment, Dalic's side can reflect on a 2018 that took Croatia to their first ever World Cup final.
"The players are very sad after the game, they were leading at Wembley and could feel the win. But they lost and that's football, we beat Spain in added time and this time we lost.
"Big picture, the law of averages evens out between teams. We can be proud of what we achieved, we deserved it, we're a small country yet we achieved great results and we're second in the world [rankings]. We have to be proud of that.
"Our first goal was to prepare for the European qualifiers and get ready for Euro 2020 so we brought in new players and managed to do that. We showed we have quality for the future, young players have a foundation for the future."