The performance by the team, which comprised of two of the individual 100m finalists, Fred Kerley and Ronnie Baker, world leader Trayvon Bromell and Cravon Gillespie, ensured the US extended its longest run without an Olympic medal in this event.
"The USA team did everything wrong in the men's relay," the 60-year-old Lewis, who won the 4x100 Olympic gold medal twice as well as seven other golds, wrote on Twitter.
"The passing system is wrong, athletes running the wrong legs, and it was clear that there was no leadership. It was a total embarrassment, and completely unacceptable for a USA team to look worse than the AAU (Amateur Athletic Union) kids I saw."
Despite the pedigree of its runners, the US team struggled with changeovers and their speed, as the anchor Gillespie -- a shock inclusion ahead of Kenny Bednarek or Noah Lyles -- struggled to make an impression in the final stint.
China ended up the surprise heat winners with a time of 37.92. Canada, with anchor 200m champion Andre de Grasse, finished second, and Italy, with individual 100m champion Lamont Marcell Jacobs, posted a national record 37.95 to also advance.
Germany and Ghana also finished ahead of Team USA to take the two fastest losers' slots in Friday's final.
The US has won the men's 4x100m relay a record 15 times at the Olympic Games, but not since 2000 in Sydney.