Pelle clawed a goal back for the hosts late on but United held on for the win.
Schneiderlin insisted his side’s focus was crucial to winning all three points against the Saints.
“We know in the Premier League it is never finished and have to be careful until the end. We were in control and it happened against Swansea and PSV. We need to learn quickly again,” he said.
“The manager reminded us this week that if we are leading and in control, then we have to keep our shape. It was strange to go into the away dressing room at the start but I had to stay focused.”
Schneiderlin himself was superb during the clash. Finding his teammates with a wide range of passing while also breaking up Southampton’s attacks, it was a typically efficient performance from the Frenchman. United are now second in the Premier League table and they will be aiming to stay there.