Nigel Adkins' men took the lead midway through the first half thanks to a Gaston Ramirez strike before the visitors levelled through a Guly Do Prado own goal less than 10 minutes later.
But, after seeing his side hold their own against the Gunners to earn a point, Schneiderlin reiterated his belief that Southampton have enough quality to stay in the Premier League.
He told reporters: "We knew before the game that it was going to be a very tough game. We knew that we would need to keep our position and that we need to keep a good shape and we did that. We were unlucky with the goal we conceded, but we put in a good shift. We give everything for each other.
|13/10||Southampton are 13/10 wth bet365 to be relegated from the Premier League
Schneiderlin's team-mate Jack Cork, who performed admirably in an unfamiliar right-back role, echoed the former Strasbourg man's sentiments and expressed satisfaction with recent results.
He said: "It was a good point. We could have nicked it towards the end. We had Stoke last week, everyone's worked really hard. It's been a busy Christmas period but we've got some points and done alright.
"Our aim was to be out of the bottom three by Christmas, and we've done magnificently to get out of there. Hopefully we can keep there during the rest of the season."