After granting Mexico a reprieve in the first half, Pitana pointed to the spot when Moreno slid in on Berg and Granqvist drilled into the top-left corner.
It was Sweden's biggest win in a World Cup match since 1994, when they beat Bulgaria 4-0 in the third-place play-off match.
He added: "I'm not going to sit here and gloat having won a match, we have a basic approach from the outset, that's what we're basing everything on".
And there are still 20 more matches to be played.
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After pressing hard for most of the first half and wasting numerous chances, Sweden finally found the net when left back Ludwig Augustinsson charged up the field in the 50th minute and angled home a left-footed volley.
An unfortunate own-goal from Edson Alvarez on 74 minutes sealed the win for Andersson's side to end above Mexico as group winners - as Germany lost 2-0 to South Korea.
It capped an emotional week for the Swedes.
Alvarez's own goal was the seventh overall of the tournament, the most in World Cup history, breaking the record of six set in 1998.
They gave the formidable Germans a tough time before Jimmy Durmaz conceded the foul that allowed Toni Kroos to score a dramatic late victor for the defending champions.
The five-time champions head into their final group match against Serbia at Spartak Stadium in Moscow needing only a draw to advance.
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That left Mexico in a perilous position, as a late German victor would have sent the Central Americans crashing out, but two injury-time South Korean goals in Kazan ensured Juan Carlos Osorio's men edged through as runners-up.
NIZHNY NOVGOROD, Russia - Already mathematically eliminated from the knockout stage, Costa Rica equalized twice in the second half, including once in stoppage time, to claim a draw and its only point of the World Cup.
Andersson had been infuriated by the celebrations of some of Germany's bench when Toni Kroos scored an injury-time victor last weekend to beat the Swedes 2-1.
But the bad news for the Swiss: Yellow cards for captain Stephan Lichtsteiner and fellow defender Fabian Schaer - their second of the tournament - meant they'll be suspended for the Sweden match in St. Petersburg.
"This is certainly not an ideal scenario", Switzerland midfielder Blerim Dzemaili said.
But Osorio was far from happy and his team will need to play a lot better if they are to go beyond the last 16 for the first time since 1986.
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Meanwhile, hundreds more people gathered at a rally outside a federal courthouse in Brownsville, Texas, in the Rio Grande valley. Capitol Police warned protesters that if they did not leave the building they would be arrested .