The crowd quickly warmed to the near era under Pochettino, 40, as Saints gave a solid display.
And Schneiderlin, 23, believes they will get even stronger once they have time to understand Pochettino's new tactics.
He said: "When a new manager comes in, he has some new ideas but we have just spent two days with him, so he has not said too much to us.
"He said that he did not want to change too much in two days but we have a few days now where we can get to know him and hopefully we can improve again.
"He seems a nice person and we know he did very well in Spain and, as a player, he was very good too, so we have a lot of respect for him."