A late Gareth Bale goal gave Spurs all three points at White Hart Lane, but Pochettino said that he was proud of his side's performance despite the result.
"Yes, we played a very good game today and we deserved to leave this game with a result," Pochettino told Sky Sports News.
"What's really important is that we competed and during long spells of the game we actually played better than Tottenham. However, it's a shame not to get anything from out of this game."
The result leaves Southampton in 14th place in the Premier League.