Italy missed out on the Mundiale for the second consecutive time after losing 1-0 at home to North Macedonia on Thursday.
The Azzurris dominated for large spells of the game but were undone by Aleksandar Trajkovski's 90th minute winner.
The result caps a disappointing low for Italy, who were crowned European champions just eight months ago.
Italy were consigned to the play-offs after finishing behind Switzerland during the qualifiers.
Jorginho missed two crucial penalties against the Swiss, contributing to their failure to qualify automatically and the Chelsea midfielder has taken his fair share of the blame.
"It is difficult to explain what happened," he told RAI Sport. "It hurts so much. I'll be honest, I am still incredulous.
"I don't think we lacked creativity, as we always dominated matches and created so many chances. Unfortunately, we were unable to finish them off.
"We played good football, we won the European Championship last summer, but unfortunately in the last few games, we made small errors and were unable to recover from them. They made the difference.
"It hurts when I think about [the missed penalties], because I do still think about it, and it will haunt me for the rest of my life.
"Stepping up there twice and not being able to help your team and your country is something that I will carry with me forever, and it weighs on me.
"People say we need to lift our heads and carry on, but it's tough."
