It is the first time England have missed out on the finals of a major tournament since 1994, when they were absent from the World Cup in America.
But Wenger pointed to the experiences of his homeland France, who also missed the 1994 tournament but were crowned champions four years later.
"It happened to France in 1994 - they did not go to the World Cup and then won the World Cup in 1998," he said.
"Here even the day after a big disappointment, there is always hope for the future, that England can win the next competition.
"Football will go on, that is for me the biggest charm in this country."
