AlphaTauri's Tsunoda has had five reprimands in 15 races, and also eight penalty points on his super-licence in the last 12 months. Twelve points in a year trigger an automatic race ban.
"Certainly I need to apologise," Binotto said after being informed by a Japanese reporter at the Italian Grand Prix that comments after last weekend's race in the Netherlands had caused offence in Japan.
"It was a mistake by using that word. There was no intention to do anything wrong. I'm very close to the victims which honestly I realise.
"I think that Tsunoda is a fantastic driver, he's a great man and we've got a good relationship between the two. We simply called him in a way to make a simple joke, but it's a bad joke."
Thousands died in Japan when a massive earthquake off its northeast coast in March 2011 set off a tsunami that swept inland and led to a meltdown at the Fukushima nuclear power plant.
Tsunoda was caught up in a controversy at Zandvoort when he triggered a virtual safety car by stopping on track, an incident that ultimately helped Red Bull's race winner and runaway championship leader Max Verstappen.
The Japanese had first stopped, suspecting a loose wheel, then returned to the pits before been sent out again only to stop with a differential failure.
AlphaTauri are also owned by Red Bull, fuelling conspiracy theories and online abuse that was widely condemned across the sport.
"We had no communication with Red Bull Racing during the race," AlphaTauri team boss Franz Tost emphasised to reporters on Saturday.
"Max Verstappen and Red Bull Racing do not need our help. They win by themselves and we need every point for ourselves. It was never programmed that we stop the car during the race because Yuki was in a good position to score points.
"We were frustrated ourselves. We could have scored points and this differential failure was absolutely a surprise. We didn’t have this problem before and therefore I don’t understand the reaction."
