Saints appeared like startled rabbits caught in the headlights in Saturday's Championship clash at Hillsborough, gifting Owls striker Luke Varney a goal in each half through two glaring pub-team blunders with the match ending 2-0.
The south coast club, who announced earlier this month that parent company Southampton Leisure Holdings Plc had been placed in administration, lie second-bottom, three points from safety with two games remaining after crashing to their 20th league defeat of the season.
Wotte, placed in charge in January following countryman Jan Poortvliet's departure, said: "It's not helping of course, but I thought we dealt with it after the Charlton game.
"It cost us the Charlton game I think at home. It was a massive three points, two games after they announced the problems and that (chairman) Rupert Lowe was stepping down.
"The insecurity isn't helping the players. If a club's struggling it's not going to help on the pitch.
"But I thought we could switch off from that and after the Crystal Palace game I thought we could do a good job today.
"It would be a little bit cheap if I blamed the result today on the off-field problems - I don't want to do that.
"The second goal for instance was just bad defending from two experienced centre-backs.
"But individual players are concerned about their future and it's better to have a secure future so they can play with more confidence.
"But that's the way it is at Southampton Football Club. That makes my job more difficult of course because you have to deal not only with the football, but also a lot of things around it."
Varney scored his first goals for the Owls in his last match before returning to parent club Derby, gleefully pouncing on two schoolboy errors which punctuated Southampton's display.
Varney held his nerve when sent through one on one with visiting goalkeeper Kelvin Davis to plant a clinical 24th-minute finish into the bottom corner after Saints defender Jan-Paul Saeijs had given the ball away to Francis Jeffers on the halfway line.
In the second half Saeijs and Lloyd James let an innocuous throw-in roll between them allowing Varney to nip in again, skate round Davis and roll the ball into an empty net in the 72nd minute.
Owls manager Brian Laws paid tribute to the crowd of 24,145 who respectfully observed the one minute's silence before kick-off in honour of the Hillsborough tragedy 20 years ago.
He said: "On Wednesday at six minutes past three I've never felt so low in a long time and on the Thursday it brought things back.
"But the supporters gave a fantastic minute's silence there.
"It's still very raw, a lot of people are still very angry. It was a fitting tribute to them."
Laws was relieved to see his side bounce back from two successive defeats to clinch only their second win in nine league matches and revealed he would be improving his squad during the summer.
He added: "We've got some good young players here and we just need some experienced players in to help them.
"We're improving the squad next season because we've improved the budget."
Wotte was so angry with referee Rob Shoebridge for allowing Varney's opening goal, which the Southampton boss believed was off-side, that he showed the official a replay on a laptop after the game.
Wotte described the goal as a "key moment".
"I went to see the referee after the game and showed him the images on the laptop and it was clearly two yards offside," he said.
Wotte added that the decision "changed the game" and admitted after the goal his side never looked comfortable in defence.