The Argentinian also criticised the officials after Papiss Cisse appeared to be offside before scoring the Magpies second goal.
Southampton are now just three points above the relegation zone.
"We put in a fantastic effort today but came away with nothing," Pochettino told Sky Sports News.
"Mistakes have cost us. At this level you can not make these, or you will get punished.
"Everything went against us today. I didn't see it at first but since I have seen it back, Cisse was clearly offside. Not only that, there was a foul in the build up."
Southampton's next game is against Queens Park Rangers on Saturday.