And he believes it will be an epic feeling when the team run out to face Saracens at a packed cinch Stadium at Franklin's Gardens on Sunday.
Saints are currently seven points behind second-placed Saracens in the Gallagher Premiership standings.
But Chris Boyd' s side go into the game on the back of a three-match losing streak in all competitions.
And they know that they can't afford to lose ground in the race for a top-four place in the Premiership.
"It is a really crucial time of the year," Vesty said.
"It's a team we'll be fighting for honours with hopefully and it's a massive game.
"It doesn't get much bigger than a full house in the first game of a new year.
"Having the Gardens full is going to be an epic feeling."
So just how are Saints going to improve to the point where they can beat a Saracens side who scored 61 points in a win against Worcester Warriors last weekend?
"We do lots of good things but being able to apply pressure and keep applying pressure and not getting bored of keeping applying pressure is how you win a boatload of rugby games," Vesty said.
"We're not consistent enough at the basics and we let teams off the hook.
"We let the pressure off and we've got to get better in that regard.
"We've got to have an understanding of what being clean and smart at the breakdown looks like and then we've got to go out on the training pitch and put it into games.
"A lot of it comes from trying to solve problems that we foresee rather than trusting our defence, which is really good, we'd rather put a hand in the breakdown and try and solve it ourselves.
"We've got to be more trusting in our defence to hold teams out for a long time.
"We're letting teams off the hook too easily."
Saracens' game plan has often proved problematic for Saints.
"You've got to respect that Sarries kick very well and it's their way of applying pressure, which comes with its challenges," Vesty said.
"We've got to win that aerial battle and then put our game on the park as well so we don't get caught up in a box-kick fest.
"We've got to implement our game.
"In anything you're trying to do, you've got to know what you are.
"We know what we are and we've got to be the best Saints we can be.
"When we are the best Saints we can be, good luck stopping it because we'll score tries and we'll stop teams scoring tries and we'll win most games."
Saracens will not only bring a shrewd kicking game but plenty of physicality, too.
"There's always a physical battle on any rugby pitch and if you don't win that physical battle you don't win many rugby games," Vesty said.
"You can have that physical battle in different ways: you can put the ball in the air and chase it, you can run big men into tight spaces or you can move the ball to space.
"You have to find the way you're going to win those battles.
"Some teams do it in a very specific big-man style and that challenge comes every week."