The 67-year-old Frenchman's remarks may further enrage Arsenal fans who are divided as to whether he should sign a new contract and extend his 21-year reign after a season of crushing disappointments.
Wenger, though, moved to make his point with regard to Arsenal's refusal down the years to match some of their rivals huge wage bills.
The London Evening Standard on Thursday had said the club had offered 28-year-old Sanchez £300,000 a week.
"You have many different opinions there," said Wenger.
"Some people tell me 'just give him what he wants', but then you cannot respect anymore any wages structure and you put the club in trouble as well.
"That is why you have to make the decision in an objective way. Always the club has to be the priority.
"I understand as well that top players is a big priority but, at the end of the day, even for important players you can only pay as much as you can afford.
"We must accept that also modern life has changed a little bit and we always had a wage schedule that was respected, but players earn so much money now that the cases have become much more individual than global."
Sanchez has cut a glum figure in recent months, apparently clashing with team-mates over their lack of fight, but has scored 22 goals this term and set up 17 others earning himself a nomination for the Professional Footballer's Association (PFA) Player of the Year Award.
However, while he has largely maintained his standards the team has not.
They have slid out of title contention and were humiliated in the Champions League but are also struggling to qualify for next season's Champions League.
Their only hope of silverware lies in the FA Cup which will see them play Manchester City in the semi-finals next weekend.