The Chilean striker is set to join Manchester United within the next 24 hours after refusing to extend his Gunners contract.
Arsenal took a similarly difficult decision to sell former striker Robin van Persie to United for £22.5m in 2012.
The Dutchman had refused to sign an extension forcing Wenger to sell him or risk losing him for free.
Selling Van Persie to direct rivals United enraged Arsenal fans, but Wenger thinks this situation is different.
“We took Van Persie when he played in the reserve team at Feyenoord," said Wenger in quotes reported by The Telegraph.
"We made a long work with him. When you get them there and, after they leave, that is the most painful.”
How Arsenal could line-up if they sign Henrikh Mkhitaryan
GETTY
“Our fans know Alexis will not extend - they have accepted that idea and the fact it will not be one-way traffic”
Arsene Wenger
The Arsenal manager hopes that signing playmaker Mkhitaryan will appease Arsenal fans to an extent.
Wenger believes the Gunners faithful will be understanding with regard to the deal the two Premier League clubs have struck.
“Our fans know Alexis will not extend - they have accepted that idea and the fact it will not be one-way traffic,” he said.
getty
getty
“It will be other-way traffic as well and that makes the whole thing a bit smoother, maybe a bit less disappointing.
"We lose a player, yes, but we could gain another player. I think one would replace the other.”
Arsenal face Crystal Palace at the Emirates on Saturday (3pm).