The Black Cats have collected just one point from their opening seven Premier League fixtures, and Vaughan admits that they need a successful start under new head coach Gus Poyet.
The 30-year-old told the South Wales Evening Post: "Every game is going to be important for us now.
"We need to get off to a good start under the new manager and pick up points as quickly as possible. Otherwise, we're going to be cut adrift at the bottom of the table."
Sunderland travel to Swansea City this afternoon for Poyet's first game in charge.