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.