Conor Murray, the Irish scrum-half, will take over as skipper and Wales lock Adam Beard will replace Jones in the squad.
It is a huge blow for the Lions to lose their leader who was set to go on his fourth tour with the composite side.
“Al has been great for me personally, made me feel very welcome in the group,” said Sutherland. “So he will be greatly missed by everyone.
“But there are a lot of guys who will step up to the plate and start taking those leadership roles.”
Sutherland can empathise with Jones having just returned to the fray himself after recovering from the same injury. The prop dislocated his shoulder in Scotland’s Six Nations win over France at the end of March. He played the first 51 minutes of Saturday’s 28-10 win over Japan in his first outing since the game in Paris.
“Al is an extremely good leader, a fantastic captain,” added Sutherland. “But I think the boys are still gelling, getting used to each other.
“That will continue for a number of weeks after a good first game.”
Dan Biggar the Lions stand-off, said the squad needed to now move on from losing their skipper as they embark on their eight-game tour.
“Obviously it’s pretty disappointing to lose your captain and your talisman five or six minutes into the game,” said Biggar who was immaculate off the tee at Murrayfield, kicking four from four conversions.
“He was pretty down in the changing room, as you’d expect. It’s one of those things, we’re lucky in the group that we’ve got a lot of good leaders, good speakers.
“But you’ve only got to look at Al’s record and experience. It’s going to be a huge loss.
“Things move so quickly on these tours. When you’re in camp, the rest of us almost have to put it to one side and look at what we’ve got.
“But obviously it’s hugely disappointing for Al and as a squad, absolutely.”