Pochettino 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."
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."
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