Pellegrini's City won the Capital One Cup on Sunday afternoon with a thrilling 3-1 win over Sunderland at Wembley.
City looked destined for their second shock cup final defeat inside 12 months when Fabio Borini gave the Black Cats a deserved first-half lead.
But Yaya Toure and Samir Nasri scored within two minutes of each other to put City ahead and Jesus Navas ended any hopes of an upset in the final minute.
City are still in the FA Cup and they lie second in the Barclays Premier League. They are two goals down in their Champions League tie with Barcelona, but Pellegrini hopes he can guide his team to glory in all three remaining competitions.
Manuel Pellegrini: "We are the only club that has the chance to continue trying to win all the competitions and this gives us a lot of confidence.
"We wanted this trophy but I don't think that anybody can think that is enough. I don't think for top players or important clubs, you are satisfied with one trophy.
"We know it won't be easy, but we are going to try."
Pellegrini reckons the memory of last year's FA Cup final defeat was one of the reasons why his team under-performed in the first half.
"Maybe what happened last year in the final was on their minds in the first half but I think that the most important thing was to calm the players and trust in them," Pellegrini said.
"I told the players they had 45 minutes to change the score. It was important for the players to be calm and they were."