The visitors were impressive in the opening half at the Etihad Stadium, responding to Yaya Toure's third-minute penalty with a goal of their own from 12 yards - scored by Rickie Lambert.
However, Southampton were undone by a controversial second for City in first-half stoppage time as Samir Nasri turned home David Silva's pass, though replays showed the Spaniard had clearly been in an offside position.
Edin Dzeko grabbed another before the break, with Stevan Jovetic rounding off the result 10 minutes from the end.
But Pochettino focus was fully on City's second, claiming that the rest of the game was immaterial given the officials' lapse in concentration.
"It's clear that the second goal completely changed the entire game, after the second goal there is nothing to analyse, we were far superior," the Argentinian said.
"We were superior to their team - Manchester City, a team fighting for the Premier League.
"Up until then you can analyse the game, but afterwards there is nothing to do it's impossible to play against a decision like that, there is nothing we can do.
"It killed off the game."
Pochettino lost England international striker Jay Rodriguez to a serious-looking knee injury midway through the first half, which looks likely to rule him out of the FIFA World Cup.
The Southampton boss had little to update on the 24-year-old's condition, confirming he will undergo scans back on the south coast.
He added: "I don't know how he's doing or what injury he sustained - we will assess him at Southampton."
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