The Chile international was powerless as his country slumped to a 3-0 defeat to Brazil on Wednesday and failed to qualify for next summer’s World Cup.
Speculation about his future continues and Wenger hopes the pressure and disappointment doesn’t affect Sanchez’s performances for his club.
“I would say you have in every generation a player who carries the pressure of expectation of a nation,” he said.
"In France, it was (Zinedine) Zidane. In England, it was (David) 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."
Sanchez’s contract expires at the season and the forward may be allowed to leave in January to avoid Arsenal missing out on a transfer fee.
Wenger’s side return to Premier League action tomorrow evening with a trip to high-flying Watford.
