That is not quite what he said, but it is pretty much in the same spirit as what Buttigieg said about trade and jobs, according to the Washington Post. The post told readers:
"Buttigieg has said six times as many jobs were lost because of automation as trade from 2000 to 2010."
This is more or less right in the same way that Nebraska will get far more rain over the course of 2019 than the rain that caused the recent flooding. And, the assertion makes about as much sense in the context of the floods as in the context of jobs lost to imports.
Productivity growth (the term that economists use for Buttigieg's "automation") averages roughly 2.0 percent annually. This means that, in a workforce of 150 million people, we lose roughly 3 million jobs a year to productivity growth. Since the workforce averaged roughly 134 million in the last decade, we would have lost roughly 27 million jobs due to productivity growth.
By comparison, we lost 3.4 million manufacturing jobs from 2000 to 2007 (before the crash) as the trade deficit exploded. So, Buttigieg can accurately say that we lost more than six times as many jobs due to productivity growth than due to trade. And, this doesn't change by one iota the fact that the huge run-up in the trade deficit devastated millions of families and whole communities in places like Ohio, Michigan, Pennsylvania, and Indiana.
It is also striking the Buttigieg is worried about automation proceeding too quickly. Pretty much the whole economics profession has the opposite concern, that productivity growth is too slow. Productivity growth has averaged just 1.3 percent annually over the last decade. In fact, the NYT just ran a column telling readers that we should expect that productivity growth will remain slow forever more.
In principle, productivity growth is associated with rising real wages and shorter work hours. It is striking that Buttigieg is apparently concerned about something that is so directly at odds with both the data and standard economics.