Roberto Mancini's side, who are currently top of the Premier League table, face Liverpool in the Carling Cup semi-final tonight.
Although the 3-2 loss to Manchester United knocked them out of the FA Cup last Sunday, Vieira says that the manner of the defeat shows the quality of the side.
"You can win games because you've got quality in your team, but I don't think you can win a championship if you don't have togetherness, hunger and desire," the Frenchman told the official City website.
"We have got the quality, there is no doubt about that, and we've now showed to everyone that we have the hunger and desire to win trophies.
"When you mix the both it can be unbelievable, so I'm really excited for the rest of the season because the way the team played against United was really good."
Vieira took up the role of Football Development Executive at City following his retirement.