City have spent close to £100 million recruiting Fernandinho, Jesus Navas, Alvaro Negredo and Stevan Jovetic as they bid to win the Premier League title back from rivals Manchester United.
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“The club has spent money in important places,” Pellegrini told reporters.
“We have the players that we need here, but we will see what happens in July and August.”
The former Malaga coach is not worried about managing in the Premier League for the first time but believes getting off to a winning start is vital.
“It’s important to make a quick start and to win the first league game because if you lose ground it is difficult to recover,” he said.
“The English Premier League is a different league than what I have worked with before, but I am not concerned about that.
“Of course it is always good to have more time, but I hope the team will be prepared.”