City had their lead cut to two points by neighbours Manchester United after suffering a first league defeat of the season at home to West Ham United.
Kompany, goalkeeper Joe Hart, midfielder Sami Nasri and defender Pablo Zabaleta were all fit, said Pellegrini, who had 11 players missing for the League Cup tie at Sunderland in midweek which meant he had to pick almost all the available first-team players.
City duly won 4-1 after leading 4-0 at half-time to restore some confidence after successive defeats by Juventus and West Ham.
"It’s important to have Vincent back," the manager said. "He’s just recovering, he’s the captain and he played very well at the start of the season."
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Eliaquim Mangala, Gael Clichy, Fabian Delph, David Silva and Wilfried Bony are still out of contention and Pellegrini said the number of injuries underlined the importance of having a strong pool of players.
The team that played against West Ham was reported to be the most expensive ever fielded by any British team at a cost of 283 million pounds in transfer fees.
"You're going to win or lose a title by one or two points normally," Pellegrini said. "In case you have these (injury) problems, you must have a strong squad.
He declined to comment on reports that City would sign English-born midfielder Luke Brattan from Australian side Brisbane Roar on a free transfer
(Reporting by Steve Tongue; editing by Clare Fallon)
