Saints struggled in the opening half-hour but eventually found their feet and put in a hard-working performance to extend their unbeaten run to six games.
And, although the manager was not too impressed with some of his side's play, he was content to take at least one point back to Southampton.
"I am happy with the single point because I don't think we played a very good game," Pochettino told the media after the match.
"I think today we lacked a finishing touch and we were quite imprecise in passing the ball, so we are satisfied with one point looking at the performance of the team.
"The goal is the same as always – we go out to try and win the game. If we can't get the three points then we try not to lose, especially our away games."
Saints did manage to find the net late in the first half when Adam Lallana poked the ball home only to be penalised for a foul on Swans goalkeeper Michel Vorm.
The decision was hotly-contested by the skipper and a number of his teammates, but their manager was reluctant to pass judgement on whether referee Mark Halsey made the right call.
He said: "I'm not sure because I haven't seen the replay on the TV, and watching from the pitch it was quite hard to see what had happened.
"Once I watch the game back on TV then I will know for sure."
Today's result keeps Saints in 12th spot, with just five points separating ninth-placed Swansea from Newcastle in 16th.
And Pochettino says the aim for his team remains to sneak into the top half of the Barclays Premier League table over the course of their four remaining games.
"I am always confident in the job that we do, and we have to now try to get three points in our next game in order to try and [get] into the first half of the table," he insisted.
"Yes, the higher we finish the better, but in able to do that we need to win our next game ahead.
"We have had a good run of six games without losing but to make the most of that we need to get three points in our next game."