The midfielder, who joined Gus Poyet's side from Brighton and Hove Albion on transfer deadline day, made his debut in the 3-0 win at St James' Park, fulfilling a childhood dream to play in the top flight.
Sunderland are two points clear of the relegation zone following the derby win, but Bridcutt believes every game until the end of the season is just as critical.
Hull City represent the next challenge for Sunderland, at the Stadium of Light on Saturday.
"Every game from now until the end of the season is a must-win game or (one we) need to get points from," Bridcutt told the club's official website. "This game (against Hull) is just as big as Newcastle.
"I'm buzzing for it; I want to impress the home fans. I'm looking forward to it and making my home debut.
"I always dreamt of playing the Premier League, to see the likes of Arsenal, Liverpool and Manchester City gives you that extra lift to do well."
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