The referee showed a straight red card to Cardiff striker Steven Thompson after 14 minutes for lunging at Bristol goalkeeper Adriano Basso as he attempted to let the ball run out of play.
That left Jones' team with 10 men against opponents flying high in the Coca-Cola Championship. And, while they worked their socks off, a battling Cardiff could not avoid defeat.
Marvin Elliott headed the only goal from Lee Johnson's 57th minute corner, leaving Jones intensely frustrated.
"I have to be very careful what I say about referees, but I felt we were let down today," he said.
"I'll leave it to the assessor to deliver a verdict, but I believe the Thompson incident warranted a yellow card at most.
"The goalkeeper deliberately put his body between our player and the ball so there was bound to be contact between them.
"There were a couple of other big decisions that went against us, including an injury-time penalty appeal, which left us with nothing from a game in which we played very well."
Bristol boss Gary Johnson admitted his side had found it difficult against the 10 men.
"Sometimes you have to give credit to the opposition and I thought Cardiff reorganised well and closed us down quickly throughout the match," he said.
"All I can say about the sending off is that Adriano has some big stud marks down the back of his calf, which swelled to twice its size by the interval.
"Of course, that can happen from a good tackle, but the referee had a good view of the incident. We had to substitute Adriano in the second half because of the challenge so it cost us too.
"It's another great result, even though we didn't play particularly well. We defended when we had to and that's all part of being a consistent side."
Bristol defeated most of the clear chances, with substitute David Noble and Enoch Showunmi going close in the dying minutes.
But a bigger victory would have been harsh on Cardiff, who claimed a handball on the goal line during a massive scramble in the final seconds of the match.
Lee Trundle, Bristol's £1million summer signing, was bated mercilessly by Cardiff fans as an ex-Swansea player, but almost silenced them with a fierce 25th-minute volley that brought a fine save from Kasper Schmeichel.
PA Sport