Sanchez's Chile stunningly missed out on qualifying for the 2018 World Cup after a 3-0 loss to Brazil on a dramatic final day in CONMEBOL on Tuesday.
Wenger, whose side return to Premier League action with a trip to Watford on Saturday, said Sanchez was among a group of players heavily relied upon by his nation – similar to Zidane with France, Beckham with England and Messi with Argentina.
"I would say you have in every generation a player who carries the pressure of expectation of a nation," the Frenchman said.
"In France it was Zidane. In England it was Beckham. We had other players in the team but it was Beckham. Why not [Steven] Gerrard? I don't know. But it was Beckham.
"In Chile it's Sanchez. In Argentina of course it's Messi. It looks like that there is somebody there in a national team who has to carry the pressure and absorb it and protect a little the rest of the team.
"It's someone normally who likes it a little bit. They like to be on the front line. Overall what does it mean? It means they have to deal with the lows as well."
Sanchez, 28, has been the subject of intense speculation for months, with the star forward in the final year of his Arsenal contract.
Wenger said he was uncertain if Sanchez would be ready to face Watford, questioning his mental state.
"He is as well in a very difficult mind. Chile just won the Copa America twice and now they don't even go to the World Cup," he said.
"Sanchez is 29 at the end of the year, so the next one he will be 33. He expected to go. Certainly [it's] a big disappointment for him.
"But I believe to play at the top level as well, it is part of dealing with that kind of disappointment."