Saints continued their good run of form by beating the Owls, who have already been relegated, to move back up to seventh in the Championship.
All three goals came from defenders, with James Bree and Ryan Manning giving them a two-goal lead before Taylor Harwood-Bellis killed any doubt in the second half.
The Owls had made things nervy after pulling one back through Jerry Yates, but Saints stood firm to extend their unbeaten Championship run to eight games.
“Very satisfied with big parts. There was a short spell when we could still improve, and it’s good to know we have to improve in some moments of the game,” said Eckert.
Saints boss Tonda Eckert celebrates a 3-1 win over Sheffield Wednesday. (Image: Cody Froggatt/PA)
READ: Saints defenders on target to record comfortable win at Sheff Wednesday
“In the end, it’s important that we take the three points today. It’s not easy to come here. We were very good in the first half, and some chunks of the second half were very good.
“Overall, I’m happy with the performance and obviously happy with the result.”
All three of Southampton’s goals came from set-pieces, with Bree and Harwood-Bellis scoring off corners and Manning finding the corner with a free-kick.
These three points also ensured they kept pace with their promotion-chasing rivals, who all earned victories this weekend.
“It’s good that we managed to bring set-pieces in our direction. We actually created more than enough on open play to score today, but we didn’t do that,” he added.
“It’s always good to have different ways of scoring, and today it was the defenders. I’m sure it will be very different for other games coming up.
“It’s good to know that we have a variety of ways to score goals. It’s crunch time now; if you do want to play for something, now is the time.”