The stuttering Saudis are midway through the final qualifying stage but find themselves second from bottom in the five-team Group B on four points from four games, with only the top two finishers guaranteed a place in the South Africa finals.
"My players have the ability, the quality and technical capability to get to the World Cup, I have no doubt about this," the Portuguese coach told Reuters.
"It has not been good so far, it will be difficult but we have to believe we can do this. I have to get this into the heads of my players, I have to make them believe.
"If they want it, they can have it, it's simple."
"We've been there at the last four World Cups, it shows we have the quality and the ability to win when it's important," said Peseiro, who was assistant coach to Carlos Quieroz at Real Madrid from 2003-2004.
"We have a big challenge and we have some big changes to make with little time. I have to evaluate the tactics and the preparation. We have a lot of hard work to do."
His job, however, has not been made easy by injuries to some of his top players, including 2007 Asian player of the year and prolific marksman, Yasser "the sniper" al-Qahtani.
"I don't want to speak about this, or how my best players are injured," he said. "I have to focus on the players I have and making them perform, that's it."
"This is totally normal in the Middle East," he added. "It's not like Europe. They change coaches all the time here.
"I'm prepared for this. I'm not thinking about when I will leave. I'm thinking about one thing -- the World Cup.
"At this moment, all my time is focused on this and I will use all my commitment and all my dedication to make sure this (qualification) happens."
