Pochettino was angry after two key decisions went against his side in their 4-1 Barclays Premier League loss at the Etihad Stadium.
The Saints boss first felt the penalty awarded to Edin Dzeko for City's opener was soft, while the hosts then benefited from an incorrect offside decision for their second goal.
Pochettino said: "I think those two decisions killed the game, that penalty we conceded and the second goal. Those two moments killed the game.
"The only positive I can think of is for the first 45 minutes we were superior to a team that is actually equipped to win the Premier League.
"But to beat a team like Manchester City, a team that is full of quality world-class players, not only do you have to have the perfect game, but also the refereeing decisions have to be fair and that did not happen today."
City got off to a perfect start as Yaya Toure put them ahead from the spot in the third minute after Jose Fonte was adjudged to have tripped Dzeko.
Rickie Lambert cancelled out that strike with a penalty of his own but City regained the lead before the break when David Silva somehow avoided an offside flag to set up Samir Nasri.
Pochettino said: "I have just seen it on TV and I don't think you can give a penalty like that after just two minutes, I think it is inexplicable it is not right.
And the second decision was clearly two metres offside. It did seem a type of game that you play at school."
Pochettino was speaking through a translator at his post-match press conference and he was initially quoted as referring to "dumb decisions", but he did not use those words.
Nasri's goal was quickly followed by a third from Edin Dzeko and Saints, 3-1 down at the break, could not respond. Stevan Jovetic made the points safe for City in the second half.
Pochettino said: "I think it can influence any player when you get a bad call like that and, of course, it did affect our players today."
Asked if he had spoken to the officials, Pochettino said: "I have already spoken to them and I am not going to speak any more to them.
"If I were to speak to them, we would have to probably repeat the match."
City may not have been at their best but the outcome was certainly a satisfactory one as they kept up the pressure at the top of the table.
Manager Manuel Pellegrini did not feel the controversial second goal was critical to his side's success.
He said: "I don't think the second goal changed the game because we scored one minute after.
"Maybe it was a mistake from the referee but we won 4-1. If we had won the game 1-0, maybe you could say it was an important mistake."
Pellegrini felt his side's second-half display was much improved from before the break.
He said: "I think it was a very different game, the first 45 minutes from the second one.
"In the first 45 minutes we didn't play well. We didn't recover the ball against a team that plays very well, has a lot of possession and has very good technical players.
"But in our worst moment, we scored three goals and I don't remember many clear chances for Southampton, only an unnecessary penalty.
"We finished the first half 3-1 and maybe that wasn't the difference between the two teams but in the second half we arranged all the problems we had. We played very well."