Pochettino believes that the win was fully earned, and that they had deserved more from their recent matches against the likes of Manchester United and Everton.
"It's an important moment in my career, training this team and beating Manchester City. We tried to break their ranks and stop the connection they had between their players," said Pochettino.
"We should have got something more from the matches against Wigan, Manchester United and Everton. Today we played well and got points we deserved."
The win lifts Southampton up to 15th in the Premier League table, six points clear of the relegation zone.