Sanchez is expected to complete his much-publicised switch to Manchester United in the next 24 hours after passing his medical with the Red Devils and being pictured wearing the club's number seven shirt.
United hijacked the bid from Manchester City with a more lucrative offer for the Chilean, but Wenger admitted that he "cannot understand" the 29-year-old's desire to leave the Emirates Stadium.
Wenger also conceded that the uncertainty over Sanchez's future had a negative impact on the team, but is confident that his side will cope in the wake of the forward's imminent departure.
"[It didn't affect] the other players, just the team. You work in a newspaper and there are periods when the atmosphere is less enjoyable than others. It is the lack of clarity. It is not losing players – teams are used to losing players. But it is fact that you have uncertainty in the group – that they don't know if he will be here or not. Once it is clear, the team gets used to it," Wenger is quoted as saying by The Guardian.
"We did what we tried to do and went as far as we could. Even Manchester City moved out of it in the end. That tells you we had no chance to give him a contract.
"I understand nothing. I cannot understand anybody wanting to leave Arsenal – but in 30 years of doing transfers you learn a lot about human beings. As a professional, it was perhaps his last contract at the top level and an important contract. After that, I accept that because we accepted that we would let him go. After that, we analyse the pros and the cons.
"There is always life. Arsenal Football Club is 130 years old and many big players have left. Will it go a bit less good? We will see but there is always life afterwards."
Sanchez has scored 80 goals in 165 appearances during his three-and-a-half-year stay at Arsenal.