Former City player Steve Thompson scored a rare goal to earn the visitors a point after Michael Chopra put Cardiff ahead on the stroke of half time.
Dave Jones said: "It was a difficult game and we probably should have seen it out but the manner we conceded so late on was very disappointing.
"It was the only time we switched off but they have good players and we gave the ball away far too easily during the second half.
"It was a soft goal to give away and you cannot leave the near post unattended. If it was from the centre of the goal then fair enough but not from that position.
"I don't think the referee had a good game as he didn't let the game flow but that is not the reason we have drawn the game as we should have gone for the jugular in the first half when we were well on top."
Despite earning a point, Eddie Howe felt his side deserved to be heading back to Lancashire with all three.
He said: "I think we deserved to win the game as we were in control apart from the opening 15 minutes.
"We bossed possession particularly in the second half and although before the game I would have been pleased with a point, now it's over I think we should have had all three.
"To concede right on half-time was a disappointment, particularly as their player had time for two touches.
"I would love to think we could make a late surge towards the play-offs but we have some tough games coming up.
"I have kept my philosophy from my Bournemouth days and inherited some very good players here so hopefully we can carry on the good work."
Howe also reserved special praise for Thompson, who netted for only the third time this season.
"Steve Thompson was delighted to score against his former club," Howe admitted. "His attitude is first-class and he has been rewarded with his goal."