The 29-year-old, who revealed earlier this summer that he had no intentions of signing a new deal at the Emirates, completed a medical ahead of what is thought to be a four-year deal at Old Trafford.
"It is another pill to swallow, we have swallowed other ones and we have always survived, but he scored 30 goals for us in the league last season, practically one every match," Wenger told TF1.
"The economic factor is the sole satisfying thing, but you don't play with money on the pitch, you play with the quality of the players. To lose a player of this ilk is tough."
Arsenal were forced to relinquish both Cesc Fabregas and Samir Nasri to Barcelona and Manchester City respectively last season.