Saints were a goal and a man up against Wolves after half an hour in their relegation six-pointer, but ended up losing 2-1, remaining anchored to the bottom of the table.
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talkSPORT understands that Southampton's owners are now considering firing Jones, who has a record of seven defeats in eight games in the Premier League.
The Welshman replaced Ralph Hasenhuttl in October, penning a three-and-a-half-year deal, but recent results and some rather odd press conferences have added to the malaise at the club.
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After a 3-0 defeat to Brentford which left his future in the balance, Jones called himself 'one of the best managers in Europe last season' while making an odd joke about Welsh women.
That went down badly in the St Mary's dressing room, along with comments that he 'compromised' and 'pandered' to top flight players, while singling out Romeo Lavia for criticism.
At full time against Wolves, there were once again boos on the south coast among disgruntled supporters, and Jones headed straight off the pitch.
"I have never done that in my life before," he said post-match.
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"In 390 games, I have never done that. But I am not sure if me going round clapping would have shown respect."
The 49-year-old former Luton Town boss then claimed that playing with an extra man made things harder for his team, a comment which likely won't go down well with fans and his superiors either.
"To me the 10 men was to our detriment because it made it a free hit for them in terms of stuff," he said to Sky Sports.
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"It added more pressure on us and it shouldn't be like that - we should then control the game.
"We had a second chance and didn't take it and it seemed to galvanise them, we had a lot of territory, a lot of balls around their box without showing the quality that we needed to win a Premier League game and then they got a bit fortunate, showed one bit of quality and they've won the game.
"We were everything that we wanted to be. That was a side that I've prepared this week and really nailed a lot of things down.
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"It's just we have to show a little bit more quality, a little bit of killer instinct, we had 17 shots, only two on target and that tells a story because we should have won the game today.
Asked if he felt he was under pressure to lose his job, Jones finished: "I couldn't feel any more pressure than I have been under this week.
"We have to keep fighting. I'm really disappointed and frustrated."