The France right-back became the latest player to join City from the London club when he signed a three-year contract after becoming a free agent.
Sagna joins former Arsenal team-mates Samir Nasri and Gael Clichy at the Etihad Stadium after a seven-year spell under compatriot Wenger in the capital.
Wenger had hoped the 31-year-old would opt to stay with the FA Cup winners, but he could line up against Arsenal in the Community Shield at Wembley on Sunday and the Arsenal boss has spoken of his regret that the defender opted to turn his back on the club.
He said: "What is tiring is to lose players to City or somebody else. You will have to ask Sagna why he chose City. I made him a proposal to stay for three years, but he chose them.
"Had he chosen a long time ago? Maybe – it looks to me like he agreed it a long time before.
"It is disappointing because he came here as an unknown and he became a French international. But I also respect Sagna because, until the last day of his contract with us, he was super-professional."
Despite the setback of losing Sagna, Wenger believes Arsenal have proved they are able to compete with their rivals in the transfer market with the big-money signings of Mesut Ozil and Alexis Sanchez.
He added: "We are less vulnerable in the market. Over the last year we have bought Mesut Ozil and Alexis Sanchez – five years ago we would have missed out on both of them."
