An Alvaro Negredo hat-trick, a double from Edin Dezko and an indivudal effort from Yaya Toure gave City a thoroughly comfortable and deserved triumph at the Etihad on Wednesday night.
The Chilean was full of praise for his side after seeing them dominate the match from start to finish.
"I think today was an important result for us to play at Wembley, it is never finished but today we have one leg in the final," he told Sky Sports.
"I think for me the most important thing was that not to score the sixth goal but the way that this team must play, it is also important not concede and that is why I am happy with how we play.
"If we play like this goals will come - but the way we played we didn't allow one counter attack from West Ham and we continued and had more chances, the way the team plays is the most important thing.
"We have the second leg in London to come but we will try and continue to play like we did here today."
Pellegrini was full of praise for his striking duo Negredo and Dzeko, but he admits he found it hard to pick out any of his players.
"I think Alvaro today made a complete game, three goals and he was a link with the midfield, who played very well too, and the whole team played well of which Alvaro is part of and Dzeko also, he works a lot for the team - they were not used to play together but the more matches they do they play better."
Pellegrini is now just two games away from possibly his first piece of silverware, but he insists he is not thinking about any silverware just yet.
"We are thinking game to game, we go to Newcastle on Sunday and continue fighting for the Premier League, in April we can talk what we can do but for now it is game by game," he concluded.
Outstanding yet again. I don't always agree with Pellegrini's teams but he does love a drubbing. Every interview he seems to emphasise goals, goals & more goals. Love him. I doth my rain soaked cap to those happy hammers fans. You the fans didn't deserve that team performance last night.- eyal&alib