Sanchez will miss out on the World Cup next summer after a 3-0 defeat to Brazil left Chile sixth in South America's qualifying group.
"I would say you have in every generation a player who carries the pressure of expectation of a nation," Wenger said.
"In France it was (Zinedine) 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 (Lionel) 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.
"Remember 1998 when Beckham has been sent off after (kicking) Diego Simeone, he has been slaughtered here, he's not been picked for the first two qualifiers after for the European qualifiers.
"He has been treated in this country like a guy who has killed somebody. These players have to take both the positives and the negatives as well."