Head coach Warren Gatland named Warburton as one of 15 Welshmen in his touring party, with 10 Englishmen, nine Irishmen and three Scots also set to travel.
McBride knows better than most what it takes to taste glory with the Lions, having done so in both 1971 and 1974 and he was quick to remind Warburton just what it will take ensure the class of 2013 follow in those illustrious footsteps.
The former Ireland second row will forever be remembered for the manner in which he skippered the side on their unbeaten tour of South Africa 39 years - a tour on which everyone spoke of unity and cammeraderie rather than national cliques or individual grievances.
"With the honour comes responsibility and you mustn't forget you have players from the four countries," McBride told the BBC.
"You don't have Welsh Lions or Irish Lions or English Lions or Scottish Lions - they're all Lions, and the first thing he (Warburton) has to do is weld them into a team and forget about the nationalities.
"After that he's obviously got to play well and lead well, not only on the field but off the field.
"And obviously it carries a lot of responsibility with it if you're going to win."
Warburton was chosen ahead of the likes of veteran Ireland duo Paul O'Connell and Brian O'Driscoll to steer the Lions ship having guided Wales to the World Cup semi-final in 2011 and Grand Slam glory in 2012.
McBride admits that he would have opted for O'Driscoll had he been in Gatland's shoes but he will now throw his support fully behind the Cardiff Blues openside and he hopes that the whole squad will follow suit.
"I must admit that, personally, I would have taken O'Driscoll (as captain)," added McBride.
"He relishes the captaincy and he's playing well, and he's been around a long time and he has a lot of experience at captaincy.
"But there you are, Warburton's the man and we wish him good luck and I hope he does well."