Manuel Pellegrini's side reached the knockout stages for the first time in their history after finishing second behind holders Bayern Munich in Group D, completing their group games with a 3-2 triumph at the Allianz Arena.
In Monday's draw City were paired against La Liga champions Barcelona in one of the standout ties.
And Begiristain - who enjoyed a playing spell at Barca as well as serving as the club's director of football - believes City are capable of ousting the 2011 Champions League winners.
"I am very confident because our manager Manuel Pellegrini knows Barcelona perfectly," he told Sky Sports News.
"We have to be ready for everything, you want to win the Champions League, you have to beat the biggest teams and Barca is one of the biggest ones.
"It is a wonderful draw, two big teams. We are happy because we're here and we'll fight for the trophy.
"Ours is a team with a lot of confidence. (The victory over Bayern) will give us a lot of confidence, not only at home but also away in Barcelona.
"The people have to be confident, because of the way we are playing, we are showing we can score in all matches."
Asked whether he thought his connection with Barcelona would have an impact, he added: "I don't think so, the most important people are on the pitch, we are happy."
