An Alvaro Negredo hat-trick, along with Edin Dzeko's brace and a Yaya Toure effort, put City firmly in control of their semi-final ahead of the second leg at Upton Park on January 21.
And after witnessing another dominant City performance at the Etihad Stadium, Pellegrini said his charges are almost in the final.
"I think that today was an important result. Football is never finished until the end but I think today we have one leg in the final," the Chilean told Sky Sports.
While City were rampant going forward, Pellegrini also expressed his delight at his team's defensive display after they limited West Ham to only a handful of opportunities throughout the 90 minutes.
"I think for me the most important thing was not to score the sixth goal, but the way that this team must continue to play. It's very important to score goals but also not to concede," he added.
"We had a balanced team today, we did not allow one counter-attack from West Ham and we scored six goals, and we had more chances to score more.
"The way the team plays is the most important thing. We have a second game in London and we try to play there like we did today."
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