Saints are six points clear of the dropzone.
"I'm very proud and very happy for the team, who deserved the victory," he said.
"I'm very happy for all the people who work with Southampton and for all the people here at St Mary's today, it has been an incredible day."
The Argentinian also felt his side were fully deserving of the three points and restricted City playing their natural game.
"I have seen that we cut the connection between their lines and have not let them play," he said.
"It (the result) has a great value. The team has deserved its victory not least because of the three goals scored against Man City."