The Saints were crowned champions on a dramatic final day as they thrashed Farsley Celtic 5-0 at St James Park and Southport beat Kidderminster Harriers 2-1.
Harriers had gone into the day as huge favourites to take the title, but they slipped up at Southport, opening the door for Brackley to go up automatically.
It ended a long wait for promotion for the Saints, who reached the play-offs in 2018, 2019, 2020 and again in 2022, 2023 and 2024 but were unable to finish the job.
"We're up there with the best part-time clubs but really, we shouldn't be beating teams like Kidderminster and Scunthorpe to the league," Cowan said.
"There's something extraordinary been done here, not just by the players but by the staff, the hierarchy and the fans as well. It's been a big, big collective effort.
"The players were excellent (against Farsley), they showed a real ruthless mentality and I couldn't be any prouder.
"We created a real intensity, a real patience because we knew we were going to have a lot of possession, we wanted to play our patterns and we did.
"We weren't fazed about anything else. What was going on elsewhere didn't interest me in the slightest until your realise the game's won.
"The feeling I've got is incredible, I can't imagine what all the good people of this club are feeling after so many years of having a go at it."
Brackley have been building a real success story in recent years, winning the FA Trophy at Wembley back in 2018.
And now they have taken another huge leap forward as they look forward to mixing it with more of non-league football's giants next season.
"Wembley was unbelievable and this is just the same," said Brackley chairman Francis Oliver.
"The last 30 minutes was sheer torture, how time goes so slowly - but I just feel so proud for the players, supporters, volunteers, everybody.
"It's just amazing."

1. The Saints are going up!
Brackley lifted the trophy at St James Park on Saturday Photo: Pete Keen



4. The Saints are going up!
The Champagne was flowing at the post-match celebrations Photo: Pete Keen

