The Premier League heavyweights proved too strong for Championship foes Leicester City at the King Power Stadium on Tuesday.
A 3-1 victory has taken them into the last four and a step closer to major silverware in Pellegrini's first season in charge.
The Chilean told Sky Sports on midweek cup progress: "Important win. For our team it was important to continue in the Capital One.
"It was important also after we beat some important teams like Bayern Munich and Arsenal to fight today. It is normal that for Leicester it was a very motivational game and that makes it very difficult to play with these teams in the cup.
"I think it is important to improve in the way that we are playing. It doesn't matter if we are playing Capital One, if we are playing Premier League or Champions League, we try to play in the same way, changing names but doing the same things."
Pellegrini shuffled his pack again against the Foxes, with James Milner and Edin Dzeko among those to stake a claim for a more regular role after combining for City's second and third goals - both converted by the Bosnian striker.
The City boss added: "That's why, for me, all of the players in the squad know that they are important.
"Maybe one is playing more than the other, but we have so many games to play in the year that all of them have an important amount of games.
"Edin was playing less than (Alvaro) Negredo and (Sergio) Aguero because they were doing very well but every time he plays, he scores and that is very important for us."
Asked what it would mean to him to make a final in his debut campaign, Pellegrini said: "First we have to win the semi-final. But I repeat that any final at Wembley is a big game and it is important to be used to trying to win all the games you are playing.
"It is important to continue in the Champions League, in the Capital One. In the Premier we are just three points behind Arsenal, so that's good for us."