The Liberty Stadium contest was a lacklustre affair, although Saints may feel aggrieved they did not come away with all three points after Adam Lallana's first-half effort was ruled out for handball following an error by Swansea goalkeeper Michel Vorm.
Nathan Dyer went closest for the hosts as Maya Yoshida cleared his effort off the line after the break, but in truth neither side showed sufficient quality in the final third to craft a winner in what was, for large parts, a tepid game.
Not that Southampton will mind too much after extending their unbeaten run to six matches.
Pochettino's side are now eight points clear of the drop zone, and well-placed to secure Premier League survival having been written off in some quarters at the start of the season.
The Argentinian said: "It was not a very good game but we are unbeaten in six games and I am happy with the clean sheet.
"Maybe we should have won because we created the best chances but their goalkeeper made two outstanding saves.
"I don't think that we lacked impetus, but we did not have the fluency we normally have.
"I don't know if 39 points will be enough for us to stay in the Premier League, we just have to go on and try and win the next game, that is always our goal."
Swansea are all but guaranteed another season in the top flight, but their campaign is tailing off as they equalled their previous longest winless run in the Premier League of five games.
But manager Michael Laudrup was keen to focus on the positives.
He said: "We did so well on occasions until the last pass.
"The last pass is so important and it is an area we could have done better in.
"I think we should have won but when you don't you have to accept a draw and look on the positive side. We had conceded two goals in each of our last four games and we have now kept a clean sheet."
His side may have drawn a blank, but there has been no disputing the impact made by top scorer Michu this season.
The Spaniard has scored 21 goals during a sensational debut season in British football, but he was not among the nominees for the Professional Footballers' Association's Player of the Year Award.
Laudrup believes his man had done enough to earn a place on the shortlist.
He said: "Every manager wants their player to be nominated.
"He has done enough to be up there, to score more than 20 goals in a mid-table team in his first season is fantastic, that's my opinion."
Laudrup also welcomed the return of Neil Taylor to his matchday squad.
The left-back was an unused substitute as he appeared on the teamsheet for the first time since breaking his ankle in September.
Laudrup said: "It is great for him. I thought it would be a good game for him and if it had gone differently he could have come on, but I did not think it was right to bring him on there with the game as it was. But it is great for him."