A 3-0 second-leg win, with two goals from Alvaro Negredo and one from strike partner Sergio Aguero, completed a 9-0 success on aggregate.
Pellegrini said: “It is very important, the final of the cup is at Wembley and it is an important cup.
“It was important the way we reached the final, winning the game, and I hope in the final we can win.”
Either rivals Manchester United or Sunderland await, with the Black Cats taking a 2-1 lead into tonight’s second-leg of their semi-final at Old Trafford.
Pellegrini is unconcerned by the outcome and said: “It is the same for me, both teams would be difficult. We will see tomorrow.”
Negredo was in some discomfort after tackling Hammers defender James Tomkins late on and Pellegrini said: “He has some problem with his shoulder.
“We will see tomorrow if it is serious. For now it is just pain, we don’t know what type of pain.”
WEST HAM: Jaaskelainen, Taylor, Johnson, Tomkins, Rat, Diarra, Morrison, Diame (Collison 89), Nolan, Joe Cole (Downing 47), Carroll (Carlton Cole 46).
MAN CITY: Pantilimon, Boyata, Lescott, Nastasic, Clichy, Jesus Navas (Kolarov 79), Javi Garcia (Rodwell 63), Fernandinho, Lopes, Negredo, Aguero (Jovetic 65).
Referee: Chris Foy (Merseyside).