In June, the Blue Samurai became the first team to qualify for the finals but the Italian's position has come under the scrutiny after Japan lost their last two international friendlies in Eastern Europe.
"It is a fact that (the team) did not play well but this is not a time to react nervously," Japan Football Association technical director Hiromi Hara said.
"We are not going to change our way of thinking on the basis of two matches."
Holger Osieck, who led Australia's successful World Cup qualifying campaign, was fired last week after 6-0 losses against Brazil and France while Croatia sacked coach Igor Stimac on Wednesday after the country scraped into the play-offs.
After sealing their berth for Brazil, Japan lost all three matches in their Confederations Cup campaign and the dip in form has continued in their recent international friendlies.
The pressure on Zaccheroni, who led Japan to their fourth Asian Cup title in Qatar two years ago, increased after the team lost to 2-0 to Serbia on Friday followed by Tuesday's 1-0 defeat in Belarus.
"It's not like (the team's performances) were a complete disaster," JFA president Kuniya Daini added. "The team struggled but the players just have to keep trying.
"When we find out what exactly is going wrong we can deal with it. The biggest problem is that things just don't seem to be going well."