The England midfielder is City's first signing of the summer and has joined the club for a fee believed to be around £15m.
"We are looking for other players. I don't know which players. I don't want to say which. Speak with Brian Marwood (sporting director)," said Mancini.
"I said I was unhappy (on Friday). It is normal. Every manager is unhappy with one week to go and you haven't bought any players.
"I hope we are working and maybe this week or in 10 days we can do something about this. I wait at this moment and tomorrow is the time to talk about new players."
City start the defence of their Premier League title at home to Southampton on Sunday.