Clarets boss Eddie Howe promised to delve into the transfer market in the coming days to halt a worrying slide down the table.
"We are monitoring the transfer market every day but it is difficult to bring players in at this stage of the season," said Howe.
"I am very disappointed with the result because I thought the lads were magnificent. That is the spirit and intensity we need to play with every week.
"I think in terms of the level of performance, there were some good performances both individually and as a team.
"We have to give credit to Southampton though because they blocked an awful lot of our attempts. I thought we defended excellently.
"We are capable of beating anybody and we have the players to do so but today highlight the lack of depth."
Southampton counterpart Nigel Adkins said: "It is interesting which way you can look at the result - it is either two points dropped or one point gained.
"At 80 minutes and 1-0 down you will have to say that it is one point gained but we had chances to win it.
"All credit to Burnley, I thought they were the better side in the first half. We made changes at half-time, which were purely tactical because we did not have enough of the ball in the first half, and one of the lads who came on has scored.
"We want to try and win every game of football. If you look at the chances in the second half, we did enough to win it."