The Clarets had several bids turned down for Stephens, who even submitted a transfer request to Brighton as he wanted to play in the Premier League.
The Seagulls realised Stephens' importance to the squad and kept hold of the 28-year-old, who then got his head down and played a key role in Brighton's promotion-winning season last year.
He put pen to paper on a new long-term deal last summer after Albion had sealed their place in the Premier League and Stephens admits he his happy with how things have panned out.
Asked how close he was to joining Burnley, he said: "Not that close, to be honest. Stuff has happened over the past couple of years and the ultimate thing was I wanted to play in the Premier League.
"I'm happy with the way it turned out and I'm happy to be Brighton player in the Premier League.
"At the time when it was all happening, I was 27, 28, and you think about if you're going to get that opportunity again. But we had a good season the following year and looking back now it's turned out very good for myself and the team.
"I just wanted to fulfill my potential of playing in the Premier League and I'm very thankful I've managed to do it with Brighton."
The Seagulls are seven points clear of the relegation zone with four games to play and Stephens feels a win at Burnley will be enough to keep Albion in the top flight.
He said: "They're good at home but we know we've got a belief within the squad that we can go there and get a good result, which will see us over the line to stay in this division."
Stephens added Brighton can use Burnley as a model to follow in the coming years if they stay up. The Clarets finished 16th last year, six points clear of the drop zone, but are seventh this year and on course to play in the Europa League next season.
Stephens said: "We've got a good enough squad to compete at this level. We look at what they've done this year and take confidence from that ourselves.
"We're only a couple of wins from the top half of the table and we're looking toward this game. If we get three points, we can start looking ahead and look for the top half of the table.
"It's tough to stay in this division but we've got a team which I think is good enough. The manager has a big belief in the squad and if we stay up this year, we can build on it for next year.
"They've come up a couple of times over the last few years and have done very well this season. If you look at clubs like that, it's what we have to aspire to do."