The Chilean joined the Citizens at the start of the month to replace Roberto Mancini, who was sacked in May.
Rodwell told reporters: "Training has been brilliant. The manager has adapted well and we've adapted well to him.
"Hopefully we can improve on the results and keep getting fitter."
City got off to a losing start under Pellegrini in their first pre-season game as they were defeated 2-0 to South African side Supersport United.