The experienced coach watched his team fight back twice in an entertaining first half. Goals from Petar Musa and Martin Baturina cancelled out Harry Kane's opening two strikes, sending the teams into the break level at 2-2.
However, England took control after halftime, with Jude Bellingham restoring their lead before a fourth goal sealed victory for the Three Lions.
Dalic, who guided Croatia to the 2018 World Cup final and the semi-finals in Qatar four years later, said his players must recover quickly ahead of crucial matches against Panama and Ghana.
"It is not easy to lose," Dalic said. "You lose your self-confidence, and that is not good.
"We must prepare very well for the next two matches. It is important that we reach the right level after this defeat. We do not have the right to make any more mistakes."
The Croatia manager felt his side had performed well in spells but paid heavily for costly errors.
"I would not say it was a bad match," he said. "There were some mistakes and England punished us for them. Two matches are still ahead of us and we have a chance to make a new start."
Dalic reserved his strongest criticism for Croatia's defending from set pieces, an area he believed had been thoroughly prepared before facing England.
"We used to be very good at defending set pieces," he said. "We knew how England would play and we worked on it before the match.
"It was disastrous, especially against a team like England. Around 40 per cent of their goals come from set pieces. We must correct that and avoid making the same mistakes again."
Despite the defeat, Dalic took encouragement from the way Croatia responded in the first half after falling behind twice. Musa and Baturina showed character to bring their side back into the contest before the break.
The turning point came shortly after halftime when Bellingham's goal put England ahead for a third time.
"After that goal, we had 10 minutes that were really bad," Dalic admitted. "We tried to come back into the game, but we could not do it.
"It was a strange match. We made too many mistakes, especially from set pieces, but I must congratulate England."
Croatia now turn their attention to a must-win Group L clash against Panama at Toronto Stadium on June 23, knowing another setback could seriously damage their hopes of reaching the knockout stages.
