Gatland's 12-year Wales coaching career will end on Sunday if the Six Nations champions lose to World Cup quarter-final opponents France in Oita.
But they have their sights set on global glory after making respective semi-final and quarter-final exits in 2011 and 2015.
Wales assistant coach and skills specialist Jenkins has been with Gatland every step of the way, playing his part in masterminding three Six Nations Grand Slams.
"His record speaks for itself as in the results, the success, the togetherness of the team and the squad and the staff," Jenkins said. "'Gats' is not just an incredible rugby coach, he is an incredible person as well.
"He brings so much to this environment, it's unbelievable, really.
"It would be incredibly sad to see him go, obviously. It would be nice if we could give ourselves another fortnight in Japan for him and for everyone involved.
"'Gats' is the same, no matter who we are playing, week to week. It is probably us he has to calm down and the rest of the coaches.
"He is an incredibly smart rugby man and knows the game inside out, and we will be prepared for Sunday.
"He's been here for 12 years, and whatever he does, everyone looks up to him and understands why he does it.
"He's a very smart operator, he does things for a reason and there is always a plan behind things."
Wales continued their preparations for Les Bleus in Beppu on Wednesday, with centre Jonathan Davies, fly-half Dan Biggar and wing George North all firmly on course to be available following recent knocks.
Jenkins added: "Everyone is getting there. There are a still a few bumps and bruises from a few of the guys when you play the amount of games you have in the period we have.
"Everyone seems okay, and it's a huge week for us and we are looking forward to it.
"It's commonsense. You either turn up or you are going home. There is no other way about it - it's plain and simple, really.
"Last time we played them in a World Cup in 2011 they turned us over in a semi-final in a very tight game.
"It will be a very tough game on Sunday, and a very tight one. We are looking forward to it, and it's why you play rugby to play these type of games."
Wales suffered an agonising 9-8 World Cup loss to France - captain Sam Warburton was sent off after just 17 minutes - eight years ago.
But Jenkins said: "What happened, happened. France beat us on the day and they were the better side on the day.
"It was a very tight game, it could have gone either way and it went their way on the day.
"You can't dwell on what has happened. You have to move on, and Sunday is a different game with different players.
"The next game is Sunday, it's against France, it's the quarter-final of the World Cup, it becomes a huge game for both sides. We need to win it to move on."