Vieira, 34, could return to the team against Juventus in the Europa League at Eastlands on Thursday night after being an unused substitute in the win over Chelsea at the weekend.
He said: "I have been happy with my form since start of season. It is difficult when you play one game every month.
"I need to work harder than everyone else to show the manager can count on me.
"I just want to enjoy myself. I am involved in a fantastic challenge with this club and really want to be part of it."
Juventus are in a period of transition like City and both teams are favourites to progress from the group ahead of Lech Poznan and Strasbourg.
Vieira, who had a season with the Turin club, expects City to edge out their Italian rivals.
"I think they are going through a difficult period. Maybe it is not the best Juventus side in the last few years but they are still a really competitive team.
"It will be difficult for us to find the space to play but we have players who can give them problems as well. Our strength is the squad. We can be competitive in every competition we are involved in."
Manager Roberto Mancini is aware it could be a pivotal week for the club following the victory over Chelsea with Newcastle to come on Sunday.
He said: "We are working to improve, like Juve. We need time. We have the same targets.
"It is an important week. It is important after beating Chelsea we try to beat Juve and then deal with Newcastle. They will be two difficult games."
Source: PA
Source: PA