Jay Bothroyd put Cardiff ahead a minute before the break with a stunning shot but the visitors levelled in the 66th minute when Stephen Quinn followed up to tap a rebound into the net.
It was a fiercely-contested match with seven players booked by referee Danny McDermid, five of those from the visitors as both sides looked to maintain their play-off hopes.
Jones felt his side should have scored more than one goal in the first half.
He said: "Chances were there to win the game and it was one-way traffic for most of the match as we battered them but one mistake has cost us.
"It was a fantastic goal by Jay but one is not enough certainly against a big side like Sheffield United and they scored with their only chance.
"I don't think the referee helped us at all tonight as they kept stopping the flow of the game with fouls and he did little about it.
"I cannot appeal against Jay's yellow card and now we have to do without him for two matches.
"Referees must be strong but unfortunately tonight he has allowed them to get away with far too much."
The tone for the match was set as early as the third minute when Paul Connolly was booked and he was quickly followed by Nyron Nosworthy.
The injury-hit Blades strung five across midfield and left Richard Cresswell up front as a lone striker but the Bluebirds were still on top in a one-sided first half.
One minute before the break Chris Burke crossed to Bothroyd and the skipper lashed a 20-yard bullet into the net leaving Blades keeper Steve Simonsen rooted to the spot.
The Bluebirds continued the same way in the second half but their defence switched off just after the hour when a throw-in was worked to substitute Mark Yeates whose shot was palmed away by City keeper David Marshall.
Quinn nipped in and tapped the ball over the line for the equaliser.
Michael Chopra struck the visitors' crossbar in the closing minutes but the Bluebirds were unable to breach the Blades' defence.
"We knew it would be tough playing in Cardiff with a patched-up side," said United manager Kevin Blackwell.
"Defeat tonight would have been very costly as far as our play-off hopes are concerned and now perhaps we can get a few players back fit as we are still in a position to fight for it.
"We worked hard for that point tonight and I know we have the right attitude so that should be recognised as it was a real achievement to get that point tonight.
"When you realise that I was forced to put on two unfit players from the bench you can understand why we are so delighted to have earned a point."
Source: Team Talk
Source: Team Talk