The midfielder joined the Black Cats earlier today on a three-year contract.
Sky Sports News have reported that the fee is in the region of £2.5m, but Poyet says that Bridcutt is value for money.
"The idea with Liam is many, many things. One, how important it is to have a British player," Poyet told the club's official website.
"It's important that we got him at that age and at the price we got him for, and he knows the way we want to play and understands the game. When you put it all together, it's a great acquisition."
Bridcutt made 151 appearances for previous club Brighton & Hove Albion.