After a week of disrupted preparation for the Swede, winner at Troon two years ago, he finished down the field on one over par.
Stenson, who missed last week’s Scottish Open, admitted he probably would not have played this week either had it been a regular tour event.
The 42-year-old said: “Obviously, the lack of preparation and practice was always going to affect the result to a very high degree this week.
“I feel like where I’m at today with the practice and links preparation and everything, that’s where I should have been Sunday of the Scottish, and I would have had a whole week of ahead of me.
“If it had been any other tournament, anything other than a major, I don’t think I would have teed it off this week.
“But it is what it is. Sometimes those things happen, and you’ve just got to make the best of it and move on.”
Stenson, who revealed he suffered the injury by banging his arm on a door, at least signed off at Carnoustie with a his best round of the week, a two-under-par 69.
Currently well outside the Ryder Cup standings, however, he has much to do in the coming weeks to try to secure automatic selection for the European team for this autumn’s clash in Paris.
He said: “I’m hoping the arm will clear up in a week or so and I can get back into playing without thinking about that and just working on my game, and hopefully I can find some form.”
Rory McIlroy feels he is still in strong contention at the Open despite dropping two shots late in his third round.
The 2014 Open champion bogeyed the 16th and 18th at Carnoustie to fall back to five under par, four shots off the lead heading into the final day.
McIlroy, who signed for a one-under-par-70, said: “I felt I did well to get to three under par for the round after 15 – it was a good birdie there.
“I would have taken three pars on the way in and would have been happy going two behind going into tomorrow.
“I’m obviously disappointed after the way I finished, but I’m still in the tournament. I’m only a few shots behind. The wind is supposed to pick up a little bit. So it will make things interesting.
“I just need to get off to a fast start tomorrow.”
McIlroy, chasing his first major victory in four years, had felt his attacking approach was paying off until his late slips and he intends to play the same way in the last round.
The Northern Irishman said: “Definitely – (the plan is to) go out and hit a lot of drivers.
“I felt like today the course was perfectly set up to take advantage of it and attack it. I tried to do that for the most part.
“Maybe my wedge play wasn’t quite as good as it should have been, but I give myself plenty of chances. I just need to regroup and get ready for tomorrow.”
McIlroy did show his frustration on the 16th after a photographer took a picture as he played a shot but he later insisted that was not a big issue.
He added: “I probably just didn’t give myself enough time to regroup after a photographer was in a world of his own.
“He was taking a photo of the crowd instead of paying attention to the golf. It’s fine. That’s one of the things that happens. There’s a lot of people out there, and it is what it is. It’s probably my fault.”
Woods has not played in the Open since 2015 due to injury and is without a victory since 2013, while the last of his 14 major titles to date came a decade ago in the US Open.
But the 42-year-old has made a remarkable return to action since undergoing spinal fusion surgery last April, and a third round of 66 at Carnoustie certainly had his legion of fans believing in what had once seemed impossible.
“It seemed like everybody was shooting six, seven under and I figured I could probably do the same and I needed to with the leaders starting at six. I need to go get it,” Woods said. “It’s one of my better rounds I’ve played. I felt I really had control of the ball.”
Starting the day six shots off the lead after two rounds of 71, Woods birdied the fourth and sixth before holing from 40 feet for another on the ninth to reach the turn in 33.
A brilliant approach to the 10th set up a tap-in birdie and despite looking unconvincing with the driver, the former world number then unleashed a superb tee shot on the 11th which finished just a few feet left of the green.
From there Woods two-putted from long range for another birdie and when he did the same on the par-five 14th, he was tied for the lead in a major championship for the first time since the second round of the 2013 Masters.
A bogey on the 16th halted the charge but Woods enjoyed a massive slice of luck on the 18th, where his tee shot seemed destined to find the Barry Burn only to take a fortunate bounce to the right to stay on dry land.
After pitching back on to the fairway Woods hit a superb third shot to two feet to crucially save par and finish a shot behind clubhouse leader Francesco Molinari, who carded a flawless 65.
Former champion Zach Johnson and compatriot Kevin Kisner were setting the pace at eight under par midway through their rounds, with defending champion Jordan Spieth a shot behind.
“It kept me in the fight,” Woods added. “If the guys get to 10 (under), five back is certainly do-able. I didn’t want to drop that last shot. I played so well today I don’t feel like I should have shot four under.”
England’s Justin Rose is a shot behind Woods after earlier equalling the lowest score in an Open at Carnoustie with a brilliant 64.
Rose, who finished fourth in the Open as a 17-year-old amateur 20 years ago, birdied the 18th hole on Friday evening to make the halfway cut with nothing to spare on three over par.
And the Olympic champion carried on where he left off on Saturday, taking advantage of benign conditions to fire seven more birdies to match the 64s recorded by Steve Stricker and Richard Green the last time Carnoustie staged the Open in 2007.
“It was massive to take advantage today,” Rose said after the lowest score of his career in any major. “I was very excited last night not to be down the road, ruing another Open opportunity gone. I picked up where I left off and it was a great day’s work.”