The Black Cats drew 0-0 at Aston Villa on Sunday despite the hosts playing most of the second half with 10 men.
Fabian Delph was sent off but Gus Poyet's side could not break them down, 48 hours after losing 3-1 to Hull.
They are 14th in the Barclays Premier League, four points above the drop zone, and Jones knows they have missed an opportunity after their 1-0 derby win at Newcastle.
"It could easily have been two wins, and that would have made it three wins on the bounce after Newcastle," said Jones, ahead of New Year's Day trip to Manchester City.
"When Villa went down to 10 men, we saw how we need to improve in the final third - create more chances and take more chances.
"At times, we looked a bit vulnerable because we were so gung ho.
"But we feel it's two points lost
The gaffer knows how disappointed we are as a collective.
"I don't think he felt the need to rant and rave afterwards
It was just a general discussion."
Jones played against Hull and Villa after overcoming hamstring problems and feels the two games prove his injury woes are over.
"Every time it happens, and unfortunately for me it's happened a few times over the last year, there's always a big inquest," the 27-year-old told the Sunderland Echo.
"You have a chat about it and you want to get to the bottom of it.
"One of the things (former club) West Brom had talked about was seeing this particular specialist.
"The Sunderland staff thought there was a need for it as well, and I had a number of injections into the nerve.
"In my eyes, it's worked to play two games in three days.
"To be honest, I knew personally that the last one was the worst one I had."
Source : PA
Source: PA