Andre Onana denied Saints striker Cameron Archer from the spot before United won via goals from Matthijs de Ligt, Marcus Rashford and Alejandro Garnacho.
Ten Hag later said: "We have to win every game and we did today.
"Sometimes you have to find a way to win. First minutes of the game we had some problems but after Andre stopped the penalty and the goal by Matthjis de Light, the game was all ours."
On Rashford's goal, he continued: "It's very important. We spoke before the game and it is so huge for him, for every striker, when the season starts you want to be on the scoring list. Now he has his first, I'm sure more will come.
"We had the chances to kill the game off, we had the chances, I don't know how many. We had several to go to 3 or 4-0."
On De Ligt, Ten Hag added: "I'm not surprised. At this moment he is not fit, he's not at 100% speed. He needs the games to go up to it. We see glimpses now and once he's there he will do much better. We are happy with him and especially today with his game."