Japan only needed to draw against a Jordan team they had thrashed 6-0 last June to secure a fifth consecutive finals appearance but were let down by poor finishing in a 2-1 reversal at Amman's King Abdullah International Stadium on Tuesday.
"We wanted to qualify for the World Cup (on Tuesday) and it is a real shame and we are all disappointed," Zaccheroni was quoted as saying by Kyodo news agency.
"We paid the price for not taking our chances. Our finishing has let us down again. We had about 10 chances and Jordan had three," the Italian added.
Shinji Kagawa, who scored Japan's goal, echoed the Italian's sentiments.
"We've lost and we are gutted," the Manchester United midfielder lamented after Japan wasted a golden opportunity to secure at least a point when Yasuhito Endo's 70th-minute penalty was brilliantly saved by Jordan keeper Amer Sabbah.
"We should have scored more goals and this game was there for the taking. We'll just have to better in our next game at home."
Japan, who lead Asia's Group B on 13 points from six matches, host Australia on June 4 and wrap up their campaign away to Iraq a week later.
A deeper gloom descended on the Australian camp after Holger Osieck's side rallied to salvage a 2-2 home draw against Oman to complicate their passage to Brazil.
Osieck fielded a side that lacked experience and urgency against Oman, leaving forward Tim Cahill slightly concerned over the remaining matches in the campaign.
"I asked for a high-tempo game. I don't want the ball thrown into the box all the time," said the 33-year-old New York Red Bulls striker, scorer of Australia's first goal and a constant aerial threat as the hosts piled on the pressure late on.
"So we'll learn as we go along but overall this is going to take time because there's a lot of young players and inexperience.
"I'm happy for the youngsters that they're getting the experience but it's going to be a difficult run in to the campaign."
In Seoul, a winning goal deep into injury time helped South Korea overcome Qatar 2-1 to revive their Group A campaign after managing just one point from their last two matches.
"It was a dramatic victory," Korean coach Choi Kang-hee said. "Because of the manner of victory, that gives the camp a lift going into the final games."
Korea occupy second spot in the group on 10 points from five games as they chase an eighth straight finals appearance.
"We know what we have to do to get to the World Cup and our desire to get there is strong. We have some rebuilding to do but at the moment the focus in on qualification," Choi added.
Group leaders Uzbekistan, on 11 points from six games, increased their hopes of securing a maiden World Cup finals appearance while virtually crushing Lebanon's hopes with a 1-0 victory over the West Asians.
"It was a difficult match and we had to fight in every part of the field. Lebanon played well in the first half and they didn't make any mistakes in defence," Uzbekistan coach Mirdjalal Kasimov said.
"We tried our best against Uzbekistan... but they were the better team," Lebanon coach Theo Bucker said.
"We are playing in the final round of qualifying for the World Cup and that is an achievement for us."