The World Cup group stage draw takes place in Qatar later on Friday, and for a second successive time, Italy's name will not be in any of the four pots.
The Azzurris missed out on a place in Qatar after losing their play-off semi-final 1-0 at home to North Macedonia.
The result capped a disappointing low for Italy, who were crowned European champions just eight months ago.
Roberto Mancini's men also missed out on qualification to the last world cup in Russia after losing another play-off to Sweden.
FIFA boss Infantino was born in Switzerland to Italian parents and has close allegiance to the European champions.
“I really want to cry," Infantino told Italian sports TV channel Rai Sport.
“For all the Italians it is sad, it is the second World Cup in a row in which the Azzurri do not participate, and if they qualify for the next World Cup it will be 12 years of absence.
“I think back to when I was a kid, the emotions of watching the World Cup in 1978 and 1982, these are the things that make you fall in love with football.
“It's sad for the Italian children, but this is the situation, only 32 can qualify and the World Cup is every four years. For now…”
Italy have won the World Cup four times, only Brazil have won more with five triumphs.
