Janne Andersson (Getty Images)
Andersson has masterminded Sweden's progress to the knockout stages as winners of Group F with Mexico also going through as runners-up as holders Germany crashed out with South Korea.
"We've done a fantastic job today with this match," he said.
"I'm so incredibly proud, almost moved at the thought of how we performed on the pitch, so disciplined. I think we've grown since our last match."
Andersson said it was "hard to describe" his emotions when Andreas Granqvist stepped up to convert the penalty either side of Ludwig Augustinsson's opener and an own goal from Edson Alvarez.
"I forgot to celebrate when he scored, I was already on the next step of my planning. You can never be sure of anything in sports, but he's very good at taking penalties."
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."
Sweden, who reached the finals by knocking out Italy in the playoffs, will play the runner-up in Group E, which could be Brazil, Sweden or Switzerland.