Sanchez nearly joined City for about £60m on the final day of the summer window, only for the transfer to collapse when Arsenal failed to sign Monaco and France midfielder Thomas Lemar.
Manchester City were believed to be favourites to sign the Chile worldwide thanks to their position in the Premier League and the relationship Sanchez already has with manager Pep Guardiola.
The Manchester United legend feels when a player of Sanchez's quality became available, it would have been wrong for the club not to try their luck for him. He also said the club is not in a "bidding war".More news: Missouri governor fighting for political life after affair
"I would not like my players, when they see me on TV or read the newspapers, (to hear) the manager talking about another (player) and thinking they are not important".
Wenger says there are two major factors that will decide whether or not they can get the other two players to renew their deals- earning money and winning trophies.
It's no surprise as to why Arsene Wenger was hell-bent on making sure that Alexis Sanchez stayed at Arsenal.
City have been tracking Sanchez for 18-months, and he has made it clear he wants to link up with Pep Guardiola at The Etihad.More news: Florida mother mistakenly murdered in love triangle gone awry, report says
But Arsenal's failure to sign Monaco's Thomas Lemar as a replacement saw the London club pull the plug on the deal, forcing Sanchez to remain at the Emirates.
As the sharpshooter has not signed a new Arsenal contract, the Gunners now face losing Sanchez for below his market value midseason or for nothing at the end of the campaign.
Wenger said: "Of course I want a quick resolution". The striker believes lack of opportunities for Liverpool could mean he doesn't make it into Gareth Southgate's England World Cup squad this summer.More news: I'm feeling better, El-Zakzaky speaks from incarceration
If a deal can not be agreed with any club, Sanchez will be able to leave when his contract expires in the summer - a situation Arsenal are keen to avoid as they would receive nothing. "But there's always a way to find a different balance".