Saints' boss Nigel Adkins saw his side score an equaliser ten minutes from the end but was questioning at the end of the game as to whether they could have gone on and won the game.
He said after the final whistle: ""With 80 minutes gone and 1-0 down away from home Morgan Schneiderlin scores a goal, and it's a point gained, but when you look at it we had a great passage of play.
"There was a great cross from Frazer (Richardson) for Rickie Lambert to head the ball down. It's a beautiful pitch here at Burnley to be fair, it bounces up, hits the underside of the bar, ricochets out and you think 'here we go.'
"Adam Lallana has a couple of crosses, a couple of headers, wide, goes through at the end, should have been a penalty - he was too honest for his own good, tried to stay up, shoots and the 'keeper saves it.
"José Fonte cross comes in, far post, misses the ball. It was five goals we could have scored after starting the second half brightly.
"Fair's fair, I thought Burnley played very well first half. We knew it was going to be tough, we talked about it, we wanted to start the game on the front foot - we wanted to get about them."
"Burnley were the better side for me first half, they were at us and we know we've got no divine right to pass the football about. They denied us that and actually had opportunities themselves first half."
Adkins brought on former Claret Richard Chaplow and then Morgan Schneiderlin to get them into the game and added: "We needed to get a grip of the football because we never had the football enough in the first half so we had to do something.
"I was happy to get to half time at 0-0, change the shape around change the formation round, change the personnel around. We started the second half brightly because we didn't look after the first half. They scored a goal which we should have defended better but that's from the dugout and I've got to see it on the tape.
"The eventuality was that they were going to score and they were going to have total control of the game. So I've changed it round and I've changed the formation and the personnel to get a grip of the football. We wanted to get Lallana in the hole and we did that.
"As the second half as gone on it shows how fit we are because we've totally dominated that. It was first half to Burnley - second half to us.
"We had four great opportunities to score and in the end Morgan has got the goal, he's got in there. It showed superb fitness from our point of view but we needed to capitalise on the chances we created.
"You're not going to get any easy games and teams are going to be right up for it, especially when you're top of the league, people are going to raise their game even more. Is a point a fair reflection of the game? I don't know, but we could have won it."
Burnley boss Eddie Howe was delighted with the response from his players, whilst disappointed we couldn't hang on and get that first home win of the season.
"I thought the lads were magnificent today and that's the sort of spirit and the level of intensity we need to play at week in and week out," he said. "If we do that, we'll win a lot of games this season.
"We gave the league leaders a tough afternoon at times and up until the last 20 minutes, when we ran out of gas, we were by far the better side. Southampton rested a lot of players in midweek and we ran out of gas.
"We found it difficult to maintain that tempo, but up until that point I thought we were worthy leaders and we should have won the game.
"I think today just highlighted our lack of depth really, which is a huge concern. We lost Keith Treacy to a tight hamstring, which he felt in training on Friday, and that was our entire squad out there. There were no pro's left over, we are so thin on the ground and it's such a difficult time of the year to bring players in.
"We are monitoring the transfer market every single day, I can assure everyone of that, but it's a nightmare time to find the right players. You are only going to bring a loan player in if he is going to go into your team. Otherwise, first and foremost the player won't want to come.
"Then you have to find the right ones and a lot of the top clubs are keeping their squads intact with the Europa League and Carling Cup and we have found it incredibly frustrating."
Howe continued: "Collectively that was our best performance of the season and there were some great performances individually. "Marvin (Bartley) was magnificent. On and off the ball his game was excellent and I am delighted for him. He's had to be patient and wait for his chance, but he grabbed it with both hands.
"He has had a really dramatic rise in football, from a few years ago, from playing non-league to suddenly playing in the Championship against good sides. He has taken every step and had time to adjust, but once he does that he flies."
Finally, he said: "In terms of a unit and trying to improve our defensive record we are getting there.
"We looked a lot more solid, but you could go through the team and everyone performed, so I'm going home disappointed. "It leaves the Burnley fans still waiting for a home win and that's something we are desperate to put right.
"I thought the crowd were really supportive today and got behind us right to the end and I can't thank them enough for that. We just hope we can give them the win that they crave and we all crave on Tuesday."