The Premier League side continued its impressive form in front of goal with a 3-1 victory at the King Power Stadium, with Edin Dzeko notching twice following Aleksandar Kolarov's fine early free kick.
City was a beaten semifinalist in the competition in 2010 and 2012 and Pellegrini is eager for his men to go all the way this time around, declaring his intention to push for every trophy on offer.
"It was a very professional win," the Chilean told reporters. "It is not easy to play three games in one week but I think the team played well. It was a good first half. We had possession and dominated the game. We played at another pace in the second but that is normal.
"It is an important competition. The final at Wembley is a big game. It is important to win all competitions you play in. Why not, if you have to play them?"
Pellegrini made eight changes to the side which beat Arsenal 6-3 in the Premier League on Saturday and underlined the importance of squad depth, particularly after Pablo Zabaleta had to withdraw due to injury.
"That's why we have a squad," the City boss explained. "It doesn't matter what competition [it is], we try to play the same way, changing names but keeping the same style.
"It is very important all the players know they are important. We have so many games to play that all of them will have an important amount of games."