The Bluebirds slipped to a second successive league defeat after the visitors scored an early goal at the new Cardiff City Stadium to lift themselves back up among the Championship pacesetters.
The Bluebirds' Scottish international goalkeeper David Marshall failed to clear Ryan Taylor's cross in the 17th minute, and Fabricio Coloccini headed home his first goal for the Magpies.
Newcastle skipper Alan Smith was sent off in the 90th minute for two yellow cards - but by then it was too late for the Bluebirds, who were second best throughout the game.
Jones was unhappy that the officials had missed a genuine penalty claim.
He said: "It was a stonewall penalty when the Newcastle player handled the ball, but if you make a defensive mistake like we did in the first half, you have to suffer the consequences.
"We had good positions to get in on goal and dominated the game for long periods, but at this level, in a tight match, you do expect the officials to get it right.
"We knew it was going to be a tough game both on and off the pitch, but we had to break 10 men down and we have to be wiser.
"I have no complaints about losing the match, but when you lose you always feel hard done by, especially when the referee has to be brave under those conditions.
"Newcastle stopped our flow and Alan Smith was probably unlucky
to be sent off, but they have Premier League players and know exactly how to put their bodies on the line when necessary."
The Magpies settled down far quicker than City, and they pinned the home side back in defence in the opening stages.
Smith bossed midfield for the visitors, and it was no surprise when Cardiff failed to clear their lines and Coloccini headed home.
Enrique and Danny Guthrie were booked in the first half, and Smith received his first yellow card in the 66th minute after clashing with Joe Ledley.
With time running out, the Bluebirds mounted a number of attacks, mainly through lively winger Chris Burke, but it was in the 82nd minute that they claimed a penalty when Stephen Taylor handled under pressure from Michael Chopra.
Nicky Butt and Geremi both went on to add experience for the Magpies as they looked to close out the game, and even the late dismissal of Smith failed to prevent them earning a deserved victory.
Caretaker manager Chris Hughton said: "These are very tough games for us, but we limited Cardiff to only a few chances throughout the game.
"I haven't seen the penalty incident, but it was a game of high tempo, and that was only one of several incidents in the match.
"I think Alan Smith was very unlucky to be sent off, and possibly his reputation went before him.
"He is in the thick of most things in the centre of midfield, and that is probably why he is singled out more than others.
"The games are coming thick and fast, but we now have to maintain the impetus as we have started well. It will be a few weeks before we know exactly how we are doing."