The Frenchman feels preventing his countrymen from causing any damage will be crucial in his side's bid for an opening-day win against Steve Clarke's Baggies at the Hawthorns
Mauricio Pochettino's side, who finished 14th in the Premier League last season, open their new campaign with a tough trip to the Hawthorns on Saturday.
And Schneiderlin knows his side will need to be at their best to stop Vydra and his compatriot Anelka, who he has admired for some time.
"It's a very tricky start," the midfielder told reporters. "I'm not sure if many of their players have left but they've also brought in some quality players and as a French guy, I do admire Anelka.
"I always thought that he was an amazing player. He has abilities that no-one else has. Some people talk about how he conducts himself with the French national team but, for me, what I see is on the pitch.
"He's just a very, very good player and for him to go to West Brom just shows their ambition, too.
"Vydra has also gone there and he was the best player in the Championship, so we know that they have good attacking players."
From a personal perspective, Schneiderlin has featured for his country at several youth levels but is yet to win a senior cap - something he has defined as a key target for the season ahead.
"There are many things that I want to improve on," he said.
"It's a World Cup year and it's going to be very important for me to be in the squad as I haven't been before.
"I want to help Southampton finish as high up as we can and I also want to play at the World Cup, so I have to have a good season. I just want to play my game and to improve."