There was a point during Vinatieri's rookie season with the New England Patriots in 1996 when Parcells told the kicker that he was "week-to-week" with the franchise because he was so inconsistent.
Vinatieri knows about Belichick's thoroughness -- not only with game planning and execution on the field, but also with players knowing everything about their teammates and coaches -- after playing under him for five seasons in New England, including three Super Bowl titles.
Vinatieiri came away a better player after his time with Parcells and Belichick, who have an ESPN 30 for 30 coming out about them on Thursday called "The Two Bills."
"They build a certain type of expectation out of their players and they know they have to know their playbooks," said Vinatieri, who is the only active player in the NFL who played for both coaches. "Both are really, really great judges of talent, both really good motivators who get their players to play well and believe in their system and get the most out of guys.
"Players know what their expectations are and to be successful in their program, you have to do X, Y and Z. You learn that way and when you go other places you bring that with you there, and if you can excel and succeed playing for them, you're going to be successful in a lot of places."
What Vinatieri respected about both coaches is that they both operate a "tight ship." One of the biggest differences between the two, according to Vinatieri, was that Parcells liked players he had a history with. Players like Keyshawn Johnson, Curtis Martin, Drew Bledsoe, Terry Glenn and Vinny Testaverde played for Parcells for multiple franchises.
"One thing I always noticed out of Bill Parcells is that he always wanted a good class of blue-collar, hardworking guys that he felt like he could win games with that way," Vinatieri said. "... When the difficult times came about he knew who was going to perform. Whatever team he was with, he would always cherry pick some of his older guys so he had his core group of guys that he appreciated and always wanted to have."
Belichick continues to prove that he's arguably the NFL's greatest head coach ever. The Patriots will win their sixth Super Bowl under Belichick if they beat the Philadelphia Eagles on Sunday.
"The X's and O's with Bill Belichick is pretty amazing," Vinatieri said. "He figures out a game plan that he would always say that he's going make the team beat us left-handed. If you have the No. 1 receiver in the league, he's going to jam him on the line, double cover him, going to do whatever and make you beat us some other way. If you're a passing team you're going to have to beat us running or vice versa. Pretty impressive the way he puts game plans together."
Vinatieri laughed when asked if the two Bills have a personality outside of their demanding style of coaching.
"Yeah, they do have another side to them," he said. "I really appreciate the structure in which they do things. I also like how hard-nosed that they are. On the other side, though, they're actually funny guys as well. The media doesn't get to see it often. They're guys with a great sense of humor. You just don't get to see it very often on the outside looking in.
"The players can appreciate what they bring to it. There's times where it's fun. They're funny, but that's a select few times. They want you to be doing your job well and when that working part is done they they let it loose. I was very fortunate to be able to play for both of them."