'Unbelievable experience' for Cobblers' Wembley hero Watson
The midfielder set the ball rolling on an incredible night for Keith Curle's men, scoring the opening goal after just 11 minutes.
Terrific Town were 2-0 up at the break thanks to Watson's goal and a Callum Morton strike, before late efforts from Sam Hoskins and substitute Andy Williams sealed an emphatic victory after Grecians' Dean Moxey had been red-carded for a bad tackle on Watson.
The match was played in a surreal atmosphere behind closed doors at Wembley, but that didn't take anything away from the occasion for Watson, who said: "It was unbelievable and a great experience.
"I am made up to be a part of this group, and all the lads fully deserve it, all the staff fully deserve it.
"It was sad that the fans couldn't be here, but obviously they have supported us all season and this is for them as well."
And he added: "We knew we had a job to do, so regardless of the fans being here or not, we had a job to do and I think all the fans will be buzzing at home.
"It would have been unbelievable for them if they could have come here and seen us put on a performance like we did, but unfortunately it wasn't to be."
The win means the Cobblers will play in Sky Bet League One whenever the new season starts, and that is a challenge Watson is looking forward to.
"Hopefully next season we can carry on and have a good season in league one for the supporters," he said.
"I don't see why we can't go into League One and have a good year, we have the quality and all of the lads are raring to go."
Looking back on his opening goal, Watson, who rifled home from 20 yards via a deflection off Exeter's Aaron Martin, said: "I felt like I was getting closed down quickly, so I improvised a little bit because I thought a shot might get blocked.
"I thought I would take an extra touch, create a bit of space and swing the left foot at it and it went in!"
The win over Exeter completes a remarkable few days for the Cobblers, who looked out for the count when they lost their semi-final first-leg at home to Cheltenham Town 2-0 just 11 days ago.
But they roared back to thump the Robins 3-0 in the second leg, and then went one better in the final.
And Watson, who missed a spot-kick with the score at 0-0 in the semi-final first-leg, said: "I don't think we were ourselves in the first game against Cheltenham, and I don't think my missed penalty helped anything!
"But in the second leg we got into our rhythm, and I think tonight we just carried it on having got a bit more confidence from that second leg.
"We knew what we had to do in that game, and then again tonight, and we just carried it on. I thought we were great."