The midfielder joined his teammates for a lap of the St Mary's pitch following our final-day draw with Stoke City last weekend.
And Cork said he was pleased to have been able to toast the season's achievements by showing his appreciation to the club's supporters.
"One of the first things you look forward to when you see the fixture list is whether your last game is at home or not," he said.
"Last year the fans were out on the pitch so there was a completely different atmosphere to [Sunday's], but it was great to go round and say thanks because last year we didn't really get to do it.
"All the fans stayed right until the end, and it's been brilliant to have them behind us all season."
Cork enjoyed a superb season in the heart of the Saints midfield, although it took some time to get off the ground after ankle and knee injuries meant he did not make a league appearance until November.
But, having forged an impressive combination with Morgan Schneiderlin, the 23-year-old played his 30th game of the campaign at the weekend – much to his satisfaction.
"It was frustrating for me at the beginning because I didn't get much game time as I was injured," he admitted, "but since then, it's been great.
"I've played in most of the games and it's turned out just the way we wanted it to. I've loved it.
"You always wonder how it (playing in a higher division) is going to turn out – me and Morgan hadn't played many games in the Premier League together.
"It took us a couple of games to get into it. Morgan has been unbelievable all season, as have all the lads.
"It might have taken us a bit of time to get used to it, but things turned out alright in the end – we've managed to stay up by quite a way, so it's been great."