Kyrgyzstan are playing in just their second Asian Cup and though they reached the last 16 in 2019, the team ranked 98th in the world they are up against one of the top five countries in the continent who regularly qualify for the World Cup.
"Miracles don't happen many times but all the people who are with me - the staff, players and those who take care of Kyrgyz football - we need to believe in such good things," Tarkovic told reporters.
"We can't lie to ourselves saying we can win because it's a tough game, but nothing is impossible in football. Teams in this tournament have shown it's possible. With some luck we can do it, we believe in it.
"Saudi Arabia have a coach with some of the best tactics in the world. We saw how Saudi Arabia dealt with Oman (in a 2-1 win) and we're preparing for this.
"We'll try our best to use our strengths and focus on Saudi weaknesses."
Kyrgyz forward Ernist Batyrkanov said there is belief in the team that they can spring an upset.
"We analysed mistakes against Thailand (in a 2-0 loss) and we worked on it. The atmosphere in the team is good, we're ready to fight tomorrow," the 25-year-old said.
"We truly believe we can win, I trust my teammates. We can give a big fight. I know we've overcome the first defeat against Thailand and we've set new goals for this match."
Saudi Arabia nearly dropped points against Oman in their group opener and needed a 96th-minute winner to take all three points.
Mancini is also not taking Kyrgyzstan lightly - despite accidentally referring to them as Tajikistan at one point in his news conference.
"I think Kyrgyzstan is a good team. We saw what happened with Iraq beating Japan. This is football. What we did in the first match is in the past. This game is difficult," the Italian coach said.
Mancini also responded to criticism that he played Salem Al-Dawsari - the squad's top scorer - out of position against Oman. The 32-year-old plays on the left wing for Al Hilal but Mancini said he could play in several positions.
"Salem can play everywhere: left wing, second striker, midfielder - that's how he plays," Mancini said.
"He can start from the left and then come inside, he doesn't always play in that channel."
