Arsenal went down to their first defeat since the opening day of the Premier League campaign, as last season's beaten finalists Borussia Dortmund beat them 2-1 at the Emirates Stadium.
Olivier Giroud cancelled out Henrikh Mkhitaryan's opener before Polish striker Robert Lewandowski scored the winner, although he was fortunate to be on the pitch having elbowed Laurent Koscielny earlier in the second half.
After three rounds of games, Dortmund top the Group F table on goal difference from Arsenal, while Napoli also joined them on six points after disposing of Marseille 2-1 in France.
"We have to look at ourselves for not being mature enough in situations like that. If you can't win the game you shouldn't lose it," he said.
His Dortmund counterpart Jurgen Klopp, who watched from the stands as he serves a touchline ban, was delighted with the result and joked about ruining Wenger's birthday.
"I am sorry about this, really. That is a problem of the date. I have a birthday in June when there are no matches. I'm always on holiday!"
Both Chelsea and Schalke are on six points while Basel, surprise winners over Chelsea in their first match, are on four points after being held 1-1 by previously pointless Steaua Bucharest in Romania.
Steaua scored a late equaliser but have now gone a record 12 home matches without a win in the competition.
