McVeigh replaced Brett Kirk as a co-captain alongside Adam Goodes before the start of the 2011 season and he invoked the Bloods' spirit in much the same way Kirk was renowned for when he laid down the law to the players at the club's guernsey presentation ceremony in Sydney on Wednesday night.
"We still have the hunger and the passion to drive this team to be the best," McVeigh said.
"Each player on this stage has talent, but what is going to set you and us apart from the rest?
"It will be a team-first attitude. We will be united as a group whether we win, lose or draw. Nothing and no one will get in the way of this. We will be disciplined in everything we do.
"We are Swans players 24/7, not when we walk through the doors of the club. Just as we are more than just a football club, we expect our players to be more than just footballers.
"We will leave no stone unturned in our quest for a premiership. That's what we are here for. Not to win a few games here or there. Not to be happy with making the finals.
"We have won four premierships in 102 years. This isn't good enough. Our supporters had to wait 72 years in between [flags]. Let's make sure that now is our time. We're not waiting for anyone.
"If you want to be a part of it, get on board, otherwise, we will leave you behind."
The Swans have welcomed 21 new players to the club since the end of the 2009 season, but confounded critics by winning through to the semi-finals last year, where they were defeated by the Western Bulldogs.
While the club has added plenty of youth to its list in recent years, it has also lost the experience of members of its 2005 premiership-winning side like Kirk, Leo Barry, Michael O'Loughlin, Darren Jolly and Barry Hall.
McVeigh, however, wasn't interested in counting the club's losses.
"People are always saying who we have lost, but have a look at who we have gained," he said.
"Players [like former Hawks Ben McGlynn and Josh Kennedy] who want to be a part of something, players who strive in our culture, players who have had to work harder than anyone because it didn't come easy.
"They are the players I want beside me in battle."
McVeigh welcomed new players who received a Swans guernsey for the first time, but even they were put on notice as the skipper rammed home the significance of the club's tradition that he felt he had been part of since he was a boy growing up on the New South Wales central coast.
"It's easy to say that it's an honour to receive the jumper, but what is hard is to honour the jumper," he said.
"Receiving this jumper tonight is one of the best feelings you can have as a player. When you hold the jumper, hold it with pride, hold it with passion and remember who has come before you.
"Want to be a part of our culture. Want to be a part of something special. It's easy to put your body in the jumper, but what's hard is to put your heart into it.
"For our new players and their families 'Welcome to the Swans' family. You are now Bloods and your journey begins'.
"It's been said a lot but we are just passing through this club, whether it's one year or 12 years. What legacy do you want to leave on this football club? Think about the opportunity you have been given.
"Do not waste your time here, otherwise we will find someone else who is willing to do what it takes."
Jarrad McVeigh is a $339,300 midfielder in the Toyota AFL Dream Team competition.
