The France right back became the latest player to swap the Emirates for the Etihad when he signed a three-year contract with the English club after becoming a free agent.
Sagna joins former Arsenal teammates Samir Nasri and Gael Clichy at City after a seven-year spell in the capital.
Wenger had hoped the 31-year-old would opt to stay with the FA Cup winner, but he could line up against the Gunners in the Community Shield at Wembley on Sunday, and the veteran coach has spoken of his regret that the defender opted to turn his back on the club.
MORE: Biggest summer transfers | Soccer's beautiful fans | WAGs
"What is tiring is to lose players to City or somebody else," he said. "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."
Fellow defender Thomas Vermaelen looks set to join Sagna in departing the Emirates Stadium, with the Belgium international poised to agree a 19 million euro move to Barcelona.
Wenger has moved to cover their departures with the signing of youngster Calum Chambers from Southampton, and the former Monaco boss is hopeful his back line will improve from an up-and-down campaign in 2013-14.
"I was concerned [by Arsenal's record against the top four]," said Wenger. "I was concerned and shocked by the number of goals that we conceded. Of course, we were Dr Jekyll and Mr Hyde defensively. We had 18 clean sheets but when we did not keep a clean sheet we let them score.
"I think it was down to confidence. Overall we were quite sound defensively but we have a good opportunity to improve that."
Despite the setback of losing Sagna, Wenger believes Arsenal has proven that the club is able to compete with its rivals in the transfer market with the big-money signings of Mesut Ozil and Alexis Sanchez.
"We are less vulnerable in the market," he added. "Over the last year we have bought Mesut Ozil and Alexis Sanchez – five years ago we would have missed out on both of them."