The Chile striker moved to rivals Man United last month after City withdrew from the chase to sign him.
Barnes said: “I think Pep made a huge statement. I like Sanchez as a player but I don't think any player is worth £500,000-plus a week.
“And after just giving Kevin De Bruyne a new contract of around £280,000 a week, Sanchez coming in on the reported wages could have upset the apple cart.
“He was also coming in halfway through the season when a lot of the hard work has already been done.
“And also, he is not a player it seems who will accept at times being placed on the bench. He appears to be a bit of mercenary, only moving for the most money."