Italy will become the laughing stock of international football if they continue to hypothesise routes into the World Cup, federation president Gabriele Gravina said on Saturday.
The Azzurri failed to qualify for Qatar 2022 after losing to North Macedonia in a play-off semi-final in March, a stunning result that has caused much upset.
Former Juventus star Roberto Baggio said this week it was "shameful" that Italy were not automatically allocated a World Cup place on the basis of their Euro 2020 triumph.
There has been speculation Italy could get in through the back door if Ecuador are thrown out, after FIFA opened disciplinary proceedings into allegations the South American team fielded an ineligible player in their successful qualifying campaign.
According to Gravina, head of the FIGC, now is the time for Italy to accept their fate, however painful it might be.
"A few weeks ago we launched a new way of working," Gravina told Italy's Sky Sport. "We said that we must work trying to be, all together, focused on regaining credibility.
"We know very well that it is not easy, and we know that there are critical issues, but credibility is linked to a very delicate phase, that is to eliminate everything that makes us not very credible.
"Allow me also to clarify the issue of World Cup repechage, which is making us not very credible. Football has winners and losers. Italy was eliminated and did not qualify, Italy does not participate in the World Cup.
"If we have to work because we believe that the rules must be changed, we will do it later. Today, Italy's out of the World Cup.
"Let's take it for granted because otherwise we continue to say things that honestly put everyone, even internationally, in a position to make fun of us."
Speaking on Friday, Italy head coach Roberto Mancini spoke of his desire for new beginnings with Italy, whose European Championship success at last year's delayed tournament has been dampened by the failure to reach two consecutive World Cups.
"The victory of the European Championship is part of the magic that are part of those tournaments. Now we have to start again and go back to that magic," said Mancini, whose team were due in action against Germany in a Nations League game on Saturday.
"I have never had this type of problem. In football, however, when you win everyone is with you and when you lose almost everyone against you. That's how it is. The restart is from now."