With a nod to the typically Scottish summer weather seen at Troon over the last two days, he added of the fear of failure: "The sun will come up on Monday anyway, hopefully".
Stenson's winning score of 20 under was a new Open record in relation to par, eclipsing the 19 under par total set by Tiger Woods at St Andrews in 2000.
Whether Phil Mickelson finishes the deal Sunday is irrelevant.
Henrik Stenson had a 2-under 69 and was at 12-under 201.
In an astounding toe-to-toe slugfest on Royal Troon's ancient, rumpled ground, Phil Mickelson and Henrik Stenson were two old men battling by the sea. It wasn't just Open records, and it wasn't just Stenson setting them, either. Stenson's final round also had echoes of Greg Norman's own final-round 64 to win The Open at Royal St George's in 1993. He can't look back at a mistake because he really didn't make any.
Stenson was simply better, converting birdies on four of his last five holes to defeat Mickelson by three strokes.
With his family all around, cancer survivor Matthew Southgate was in tears as he approached the 18th green at Royal Troon. All the British Open lacked Saturday was a victor. I went to go get it.
"I felt like this was going to be my turn", said the 40-year-old Swede, abandoning his usual comic banter for a more serious tone.
"I knew he wasn't going to back down at any point, and in a way that makes it easier for myself", Stenson said.
The record-breaking Iceman never froze on the biggest stage of them all with a 50ft putt for birdie on 15 proving the knockout punch to the American's challenge. In a round that seemed more match play than stroke play, Stenson hit 79 percent of his fairways, 89 percent of greens in regulation and needed just 27 putts in the final round.
No one else is even close. Barely believable was the score of third-placed JB Holmes, who was a full 14 strokes behind Stenson on six under. Like it did on Thursday and Saturday.
Trading birdies and making few mistakes, the two were tied through the 13th hole, and then Stenson generated two enormous roars from the huge galleries. Mickelson managed four birdies and an eagle on Sunday, but Stenson overpowered him with 10 birdies.
The lie was OK, he chipped out sideways and nearly matched the birdie of Stenson, which dropped Mickelson out of the lead for the first time since his 14th hole Thursday. Mickelson made a brilliant up-and-down after missing the green with his approach, almost holing out a chip over a bunker.
Mickelson nearly chipped in for another birdie on the second after a wayward approach, but it was Stenson who found the bottom of the cup from 15 feet to draw level.
He then went back in front at the third after rolling in a 20-footer for another birdie. "Some days it's hard and it looks bad, like it did today".
Stenson took the lead early on the front line, Mickelson regained it, but the critical hole was 17 where Stenson birdied and Mickelson bogeyed.
It looks to be a two-man competition.
Stenson had the lowest round in the field Friday and Saturday.
"How are you, Henrik?"
They both smiled and shook hands.
Jordan Spieth has snapped an unwanted streak at the British Open.
Four Swedish golfers have won female major titles, led by Annika Sorenstam with 10 championships.
Here's the full final leaderboard from Troon. But it was Stenson - seeking his first Grand Slam win - reeling off three birdies in a row on holes 14 to 16. It was his best round in a major since a 66 in the opening round of this year's Masters.
Now it's on to the PGA Championship in less than two weeks, the schedule compressed because of the Olympics.
This was supposed to be a British Open farewell for Colin Montgomerie.
This one was more like the 39-year-old showdown between Watson and Nicklaus at another course in the British Open rotation, the one 25 miles down the Scottish coastline. Runner-up Mickelson shot a six-under-par 65 with not a single bogey and yet came up short to an opponent who was an incredible eight under on the day. That was a change in his thinking before the tournament, when he indicated he wouldn't go through qualifying again. Even that peeked out a bit over the final nine holes, when conditions softened a tad.
"We just finished, so I'm. trying to find my bearings here", Stenson said after being awarded the Claret Jug.
Looking to become the first male Swedish player to win a major, Stenson carded a third round of 68 to finish 12 under par, a shot ahead of playing partner Mickelson, who at 46 would be the fourth oldest victor of any major and oldest in the Open since 1867.