United came from behind to pick up a point after Rickie Lambert had put the hosts ahead, with Juan Mata's excellent free-kick levelling the scores in the second half.
After the game, Giggs lauded the noisy contingent of fans who made the long trip to the south coast, and expressed pride in the players after a difficult campaign.
"It’s obviously been a frustrating season, but I enjoyed that second half," Giggs told MUTV. "The players and fans were brilliant, and I didn’t want it to end. Southampton probably had the better of the first half, but as the game went on there was only going to be one winner. I’m really proud of the players today.
"The fans have supported us all throughout the season and they showed it again today; they never stopped. On behalf of the players and staff, I’d like to thank them. They’ve been brilliant this season; obviously they’ve been lucky to win so much over the years, but this year hasn’t been our year. As I’ve said before, we’ll come back bigger and better.
Giggs also had his say on the two goals at St. Mary's, after captain Nemanja Vidic appeared to be fouled in the build-up to Lambert's opener.
"I thought that Lambert caught Nemanja with an elbow," he added. "I don’t know whether or not it was intentional,