The 34-year-old Argentine was the hero as he saved three penalties to help City secure a 3-1 shootout win after the game had finished 1-1 after extra time at Wembley Stadium.
"I would prefer to lose a title than lose my word. My word is more important than football... I'm happy to win it that way with Willy as a great hero," Pellegrini told British media.
"Maybe most of the media were waiting for him to make a mistake and criticise my decision but I promised he would play both cups... But I never lost trust in him because I know how good a player he is."
City, who are fourth in the league nine points adrift of leaders Leicester City with a game in hand, visit ninth-placed Liverpool on Wednesday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Ken Ferris)
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