The Chile striker had been expected to join his international teammate at the Etihad Stadium after the Citizens submitted a £60m offer for the player.
"He went from happiness to bitterness in a few hours, although it's all in the past now," Bravo told Sky Sports News after Man City's 5-0 win over Liverpool on Saturday afternoon.
"The transfer didn't happen because a player didn't go to Arsenal and everything collapsed. We would have loved to have him here, but the market gives you these time limits and the rush is not good.
"This time it was not possible, but hopefully we will have him here in the future."
Sanchez came on as a substitute in Arsenal's 3-0 win over Bournemouth on Saturday and his 75th-minute introduction prompted a chorus of boos from supporters.