The Black Cats lost their first match in their campaign to Queens Park Rangers before the international break, and were forced to rally from behind twice to earn a draw against Mauricio Pochettino's side.
O'Shea thinks that spirit will stand his side in good stead for the rest of the season, starting this weekend against Burnley.
He told the club's official website: "It was very important to return with a positive result, especially after the defeat to Queens Park Rangers because we had the international break straight after and that was the frustrating part.
"Tottenham played very well on the day and we did very well to hang in as we did, we finished the game strongly and I think overall we have to be satisfied with a point.
"Moving forward we know the stuff we have improve on and work on going into the game against Burnley."
Sunderland are 15th in the Premier League after four matches this season.