Belichick said that Gostkowski keeps impressing him every year and that the player has a perfect attitude in training and on matchdays.
"I think, it's maybe a little bit like Tom Brady," Belichick told the club's official website. "He gets a little bit better each year, but he started off at a pretty high level. He's had a lot of great years for us and individual plays.
"He continues to work hard at his job, his training, his conditioning, his technique, obviously the execution with his other teammates on field goals.
"He just becomes a better student of the game, more knowledgeable, more experienced, better situational player. It wasn't like it started at a low point. It started at a pretty high point and it's gradually ratcheted it up a little bit."
Gostkowski has played for the Patriots his whole career, having been drafted in 2006.