The Gunners claimed a 5-2 victory over Everton at Goodison Park on Sunday which marks only their first away league win of the campaign.
Wenger admitted to being concerned when the Toffees took the lead in the encounter but is happy that his players remained calm and focused to claim all three points.
"We should have been 2-0 or 3-0 up, but we were 1-0 down. We didn't panic and maintained our focus. Once we equalised, it was all us for the rest of the game," the Frenchman told reporters.
"I was [concerned] because recently we've been punished for every mistake we make away from home. But I knew there was a long time to go. Our away performances this season have not been rewarded."
The result sees Arsenal climb up to fifth in the Premier League table.