City beat West Ham 6-0 in the first leg two weeks ago but were ruthless in a 3-0 demolition of the Hammers as Alvaro Negredo scored twice and Sergio Aguero also netted at Upton Park.
Pellegrini said: "It's not easy when you've won the first (leg of the) semi-final 6-0.
"It was important for them to play not with the other score (in mind), to play the game we did.
"I'm very proud of the team. We arrived in the final winning the five games with 19 goals scored, with just one goal conceded.
"Always a final at Wembley is a very important final and I'm very proud of the team that we are still in four competitions.
"We are not thinking about that (winning all four competitions). We are thinking just to win every match.
"Now we've finished with the Capital One Cup until March. It's very important to continue in the FA Cup, so we must win against Watford on Saturday.
"We'll continue with the same winning and ambitious mentality."
On form, it appears a quadruple is not beyond a scintillating City, but Pellegrini vowed only to continue playing in the same vein.
He added: "We have a lot of work to do. In the FA Cup we are just in the fourth round. In the Champions League we have a tough game against Barcelona. The Premier League's very close and it will still be close till the end between four or five teams.
"At the moment we are happy the way we are doing things. We must continue in the future the same way."
Pellegrini has never been to Wembley as a manager, but visited the National Stadium "three or four times", the first in 1988.
City were clear favourites for last May's FA Cup final, but lost to Wigan.
Pellegrini is unconcerned who his side face on March 2, with the prospect of a Manchester derby in the final if Manchester United can overturn a 2-1 first-leg deficit against Sunderland at Old Trafford on Wednesday night.
"Wembley's special for everyone," Pellegrini added.
"Both teams would be difficult. Maybe everybody thinks Manchester United would be our rival in the final, but Sunderland has options."
West Ham manager Sam Allardyce was left to lament further injuries as they lost 3-0 to Manchester City in the League Cup semi-final second leg.
Coming into the tie with a 6-0 first-leg deficit, it was a matter of pride for the Hammers, but their evening was made even worse as midfielders Joe Cole (groin) and Mohamed Diame (knee) went off.
Allardyce, who handed Andy Carroll his first start of the season, said: "Joe's shouldn't be too long. Mo's looked more serious - and until a scan we don't know - but (the medical department) are saying it may not be as serious as first thought.
"Still I think he would be out for a little while."
Allardyce bemoaned his side's defending and referee Chris Foy's decision not to award a penalty when Ravel Morrison and Joleon Lescott tangled in the box.
"When you let Negredo in with a free header in the first minute at the far post, there's nobody else to blame but your defenders," the Hammers boss added.
"We got a really good response off that when Kevin (Nolan) scored, but unfortunately that was offside.
"We should have had a penalty in the second half. There's no doubt about that, but the way things are going for me, I think if one of Man City punched one of our players in the face in the box we wouldn't get a penalty."
West Ham's focus now turns to their fight for Premier League survival, something Allardyce believes hinges on the fitness of his players and new signings.
Ricardo Vaz Te, Guy Demel, Joey O'Brien, George McCartney and Winston Reid are all nearing returns.
"If you give me all them fit from as quickly as possible until the end of the season, I think we'll come out of this," Allardyce said.
"Forty (points) is the safe zone over more than 10 years now. It's got to be 22 points minimum for me in the last 16 (games)."