The Scot, who lost star Mikel Arteta to Arsenal at the end of last month, spent nothing on transfer fees this summer, while opposite number Roberto Mancini brought in Sergio Aguero, Samir Nasri and others for almost £80m.
"This is like going into a gunfight and I have got a knife," Moyes said. "I am going to have to do the best I can.
"We have to find a way of stopping Man City. It was the same last year and we won the games. It was the same in that we needed to go there and find a way of stopping them doing what they do but at the same time also playing our own stuff.
"I thought they were better last year on the year before and this year they are better again."
Manchester City dropped their first points of this year's Premier League campaign in a 2-2 stalemate against Fulham last Sunday.