Sanchez's future at the Emirates Stadium seemed bleak in the summer with just a year left on his current deal and no indication of the Chilean putting pen to paper.
Manager Arsene Wenger remained adamant that Sanchez would remain with the Gunners, however, was said to have been ready to accept City's deadline day £60m ($77.7m) offer on the condition that they can sign a replacement.
Monaco's Thomas Lemar was seen as the replacement, but his rejection of a move to north London acted as a domino effect, effectively ending Sanchez's hopes of a last minute move to Manchester.
Speaking after coming on as a substitute in City's crushing 5-0 win over Liverpool, Bravo spoke about how the mood of the former Barcelona player changed in a few hours.
"We were talking in Chile," Bravo said, as quoted by The Mirror. "He [Sanchez] went from happiness to bitterness in a few hours, although it's all in the past now."
"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 have him here in the future."
Sanchez made his first appearance of the season for Arsenal later in the day against Bournemouth, as he came on as a substitute for Danny Welbeck where he received a mixed response, despite there being more cheers than boos.
The 28-year-old was lively, however, but was unable to add to the scoresheet as the Gunners ended a dominant performance with a 3-0 win.