Sergio Aguero finished off a delightful move to put City in front after 28 minutes and Yaya Toure added a second with a powerful strike seven minutes from time.
Andy Carroll reduced West Ham's arrears when his shot was fumbled by Joe Hart, but it came too late to threaten City's victory.
Mancini was nevertheless frustrated by a series of missed chances and urged his players to be more ruthless rather than always searching for the perfect goal.
He told Sky Sports: "It was important to win. I am happy for this victory, but we could have scored four, five or six goals.
"We scored a fantastic first goal, but sometimes it is enough to put your foot through the ball. Sometimes we want to be too beautiful."
Mancini also played down fears about Hart after the England goalkeeper appeared to be struggling with a back injury towards the end of the game.
When asked if Hart was okay, the Italian responded: "I think so."
It was City's first game since Manchester United were confirmed as champions on Monday, and Mancini is keen for his men to stay focused for the remainder of the season.
He explained: "It is important for us to finish this championship well because we need to win the next three or four games to finish second, and then try and win the FA Cup final."
Mancini also reiterated that he would try and strengthen his squad during the early part of the summer to give City the best chance of success next season.
"It is important to move quickly because there are a lot of teams that want to buy players," he said.