Roberto Mancini's men will take on Real Madrid, Ajax and Borussia Dortmund, the champions of Spain, Holland and Germany respectively.
Vieira said: "You can't get much worse than that, it's a really tough, a really difficult group, the hardest group of all of them. But when you look at the football the prospect is really exciting. The players will be excited to play Real Madrid - the first time Manchester City will ever have played Real - and the fans will love it to play them and Dortmund and Ajax."
Chelsea, the defending European champions, will have their work cut out in Group E along with Shakhtar Donetsk from Ukraine, Serie A winners Juventus and Danish champions Nordsjaelland, but should progress.
Manchester United and Arsenal have more seemingly straightforward tasks. The Gunners are in Group B with Schalke, Olympiacos and Montpellier, while United will take on Braga, Galatasaray and CFR Cluj in Group H.
There are a couple of glamour ties in prospect for Celtic in Group G as they face Barcelona, Benfica and Spartak Moscow.
For Manchester United manager Sir Alex Ferguson, it is a chance for his side to make amends for the "stupid errors" they committed in Europe last season, but he warned there will be a hostile environment in Turkey when facing Galatasaray.
"We have the experience of playing against Galatasaray in the past and we will always remember the 'Welcome to Hell' banners," Ferguson told his club's website. "So it's always a difficult type of match.
"We have drawn Portuguese clubs a number of times over the past few years - the likes of Benfica, Sporting [Lisbon] and Porto - so we have the experience of playing in Portugal on many occasions. Braga are one of the improving teams in that country.
"We've never played Cluj before but, after the experience of last year, we don't want to make any stupid errors this time. We will play our strongest team to make sure we get through."
Source: PA
Source: PA