The Asian champions came from behind to beat Costa Rica 3-1 at Raymond James Stadium in Florida on Monday.
After trailing 1-0 at the half-time break, Japan recorded their fourth consecutive win thanks to goals from midfield trio Yasuhito Endo, Shinji Kagawa and Yoichiro Kakitani.
Zaccheroni is under no illusion Japan and especially their strikers must be more clinical in front of goal if they are to make an impact at the FIFA World Cup, where they will face Colombia, Greece and Ivory Coast in Group C.
Speaking ahead of Friday's return to Raymond James Stadium for Japan's final warm-up match before their World Cup opener against Ivory Coast on June 14, the Italian said: "We are still in the training camp here and I think the players' condition is all right.
"I appreciate the players for their positive mental approach to their play.
"For the next two weeks leading up to the World Cup, we have to improve our concentration and mentality that will lead us to making the most of our chances, especially when it comes to our finishing."
Japan are unbeaten in their past five games, having drawn against the Netherlands (2-2) and beaten Belgium (3-2), New Zealand (4-2), Cyprus (1-0) and Costa Rica since qualifying for the World Cup.
And the Asian giants will be boosted by the news that Zambia's number one goalkeeper Kennedy Mweene will miss the game due to injury.
Mweene, capped 79 times by the national team, sustained a hamstring injury while playing for South African club Mamelodi Sundowns in an invitational tournament in Namibia.
Zambia have won four of their past five games in all competitions but are yet to beat Asian opposition in three recent fixtures.
The African nation have lost to Jordan (1-0), Saudi Arabia (2-1) and South Korea (2-1) since August 2012.
Though, Japan will have to be cautious of Patrice Beaumelle's men, who stunned the world when they won the 2012 Africa Cup of Nations after prevailing on penalties against Ivory Coast.
