Erling Haaland struck on five minutes, but Saints remained in the game thanks to their own spirit and some wayward City finishing.
After the win, Bernardo admitted: "We have a lot of respect for all the teams in the Premier League. These guys we played today, I watched the games they played in the season and I think they deserve a lot more points than what they’ve got.
"They press high, they try to build up with the ball. It makes it very difficult to press them because if you go man-to-man in the middle then it’s not easy for our defenders. Tough game for us but very happy with the three points.
"We’re used to that when teams defend deep against us which makes it more difficult, we have to be patient. We are used to that. We had our chances to score three or four goals to make it, but they deserve a lot of credit for what they did here today."