Andrea Orlandi and Will Hoskins delivered two fine goals at the Amex Stadium but it was the industry and combativeness of Bridcutt that secured the man of the match award for the 23-year-old midfielder.
Poyet fears that Bridcutt has become highly sought-after and insists he would even hold his own at Spanish giants Real.
"Yes I am worried by Liam's performance. Other clubs can ask about him because it's part of the game," the Seagulls manager said.
"If I was coach of Real I would take him because he deserves to go to the highest level.
"As a holding midfielder, there is no better player in the division. So he is quite expensive.
"The best thing about Liam is that he understands me to an incredible level. The way he understands what I want from him is spectacular."
Brighton are one win away from the play-offs in the Championship and Poyet has ruled out offloading their best players.
"Now that we are at the same level as the rest of the teams that everyone is talking about, our players are expensive, I don't put prices on them but we're not a selling team anymore."
Newcastle's early exit from the FA Cup is compounded by a troubled Premier League campaign that has left them only two points above the relegation zone.
The club has endured a terrible run of injuries and manager Alan Pardew admits they are paying the price for their inactivity during the summer transfer window.
"I never thought we'd be in this position. We've been terribly unlucky, but we should have brought in one or two more players to give us cover," he said.
"We're paying the price now, but the window is open and it gives us an opportunity to strengthen."