Goals from Sergio Aguero and Yaya Toure secured the 2-1 win as Andy Carroll's late strike was not enough for the Hammers.
City were comfortable throughout much of the game but Mancini wanted more goals - something he says has been an issue for his side.
He said: "I'm happy for this performance. I'm unhappy for the goals we missed as we could have scored more goals but this has been our problem this season.
"West Ham is a good team and have had a good season but today we deserved to score four, five or six goals."
The win maintains City's bid to finish second in the table behind champions Manchester United.
Man City last week