Japan face further fixtures with Group C rivals Colombia and Greece respectively, and Zaccheroni says that the Blue Samurai are capable of progressing to the last 16 despite a first-day hiccup.
"The players gave 100% but we weren't cohesive enough," he told reporters at full time.
"After we took the lead, we did go on the back foot, but that was because of our opponents' attacking qualities - not through our own choosing where they really pushed us back.
"We weren't aggressive enough and we need to improve on that because we've been playing better than that – and we can play better than that – and we'll work on that in our next two games."
Zaccheroni's side face Greece on Thursday.