The 2022 World Cup third-placed finishers were under pressure to beat Albania, having suffered a 3-0 defeat to Spain in their opening match at this summer's European Championship.
Qazim Laci sent Albania ahead in the 11th minute of the contest, but Croatia managed to turn the match around in the space of two second-half minutes, with Andrej Kramaric registering before Klaus Gjasula scored an own goal.
Dalic's side were on the verge of picking up a valuable three points in Hamburg, only for Gjasula to then score at the right end to hand Albania a 95th-minute leveller.
Dalic criticises players for late Albania equaliser
The Croatia manager has been critical of his side for their "error" in dropping back, with the 57-year-old revealing that the instruction had been to push forward in search of a third goal.
"We wanted to drop deep without any need to do so," Dalic said in his post-match press conference. "We didn't tell them to drop deep, we wanted them to score the third goal, to press.
"So it was weird, it was an error. We shouldn't have allowed the opponent to come onto us. This added time was really bad, there was a struggle without any need to play like that."
Croatia sit bottom of Group B on one point and will have to beat Italy in their last match in the section on June 24 to stand a chance of progressing to the knockout round of the competition.
"This is a different tournament, a different story," said Dalic when asked about the national side's recent successes, having finished second at the 2018 World Cup and third at the 2022 competition.
Dalic admits Euro 2024 has been "a struggle"
"We didn't expect to have such a difficult story in these two matches so it's been a struggle. Maybe that's the way to get out of it even better. The World Cup was two years ago and our players are getting older.
"This tournament, it's been difficult. Portugal, it was difficult for them against Czechia, England against Serbia, so this tournament is very open and the teams are pretty equal."
"The most important thing is we are still alive, we have to go for the win against Italy."
Despite their recent success in the World Cup, Croatia have failed to make an impression in the European Championship, with their best showings in the competition coming in 1996 and 2008, when they reached the quarter-finals.