The European champions missed out on automatic qualification to the Mundial following a 0-0 draw with Northern Ireland in their final group game and Switzerland duly took advantage to top Group C.
Italy have now been consigned to the play-offs, where they will face North Macedonia on Thursday, with the winner of the tie set to face either Turkey or Portugal for a place in Qatar.
Italy also missed out on qualification to the 2018 World Cup in Russia after losing their play-off to Sweden.
The Azzurris face the prospect of missing out on a second consecutive World Cup, but Mancini is optimistic a place in Qatar will be secured.
"We should not take the first game for granted. It won't be easy and, in case we win, we'll have four days to prepare for the final," he told reporters at a news conference on Monday.
"We have built a solid base, we are positive and we must think that everything will go well. We have two tough games ahead. We were not supposed to be here, but it happens to struggle sometimes.
"We must continue playing as we've always done. We didn't reach our targets by coincidence. We didn't want to play these games, but the lads are feeling well and that's important.
"I am optimistic because I have players who won the Euros starting from nothing when nobody believed in it. We must think about what we did to have more self-confidence, the team is solid and with quality.
"Our target is to win the World Cup, and in order to do it, we must win the next two games. We want to go to the World Cup to win it."
