Caballero, a close-season signing from Malaga, was retained for Saturday's 4-2 top-flight win at Hull City after starting in the midweek 7-0 demolition of Sheffield Wednesday in the League Cup.
City manager Pellegrini played down the significance of his decision, though, stating that it was important to rotate his goalkeepers.
"I think that for Willy Caballero, it was important to play two games in a row," he said.
"Also, Joe Hart had played eight games in 32 days, so it was a lot of games for a goalkeeper, it's good for him to work normally, and I have a squad with 22 or 23 players and I made the rotation that I believed is better for the team.
"On this occasion it was good for Willy to play."
It is not the first time Hart has found his position at City under threat, with the 27-year-old having deputised for Costel Pantilimon in seven league games last season following criticism of his form.
Saturday's KC Stadium triumph kept City five points behind leaders Chelsea.
