The Gunners have gone four games without a win in the Premier League, a run of results that has seen in-form Everton overtake them and move into the Champions League qualifying places.
Arsenal will look to move back above the Toffees for 24 hours at least when they take on West Ham United at the Emirates on Tuesday, and Wenger is confident that they can build upon their penalty shootout win over Wigan to make a strong finish to the season.
"There was a lot at stake for us. You know how it is today in football - had we gone out of course we would have been tremendously questioned and I knew it was a turning point of our season," Wenger is quoted as saying by PA.
"To go out on Saturday would have been very difficult, but we have shown resilience and nerves, and that is an important quality at the top level."
Arsenal are currently two points behind Everton in the Premier League table, with the Toffees not playing until Wednesday.