Cardiff were 2-0 ahead with five minutes left before the Clarets clawed their way back to 2-2, leaving the Bluebirds 10th in the Championship.
With only five goals in eight games - all from set-pieces - Slade recognises his team must improve in attack.
"I thought we were a threat in open play. We've just got to be more ruthless in the box," he said.
"I thought we were creating chances, even in the second half I think [Joe] Mason went through once or twice. On another day, we'd probably finish those.
"We've got to be scoring more goals when we get those opportunities in open play.
"It is really really hard to take. We were the better side for long periods and the better side didn't win."
Second-half substitute Mason was the last Cardiff player to score in open play, tapping in for the opening goal when Slade's side drew 1-1 at Brighton on 3 October.
It was from the reliable source of set-pieces that Cardiff built their 2-0 lead against Burnley, Aron Gunnarsson nodding in from Joe Ralls' free-kick and Peter Whittingham's corner finding the head of Sean Morrison.
Seemingly coasting at 2-0 up with only five minutes left, Cardiff capitulated as Burnley fought back with a close-range strike from Rouwen Hennings and an own goal by Matt Connolly.
It was Connolly's injury-time aberration which most dismayed Slade, as the former Queens Park Rangers centre-back dragged Michael Keane's header over his own line.
"The second goal was just bizarre. It was going a mile wide but then it came off Matthew and rolled right into the net," said Slade.
"It was a crazy equaliser. You could see how much it hurt the players who had worked so hard to get the better of a very good team.
"That goal is the difference of being between sixth and tenth and it's pretty hard to take."

England, who have never won the competition, were knocked out at the group stage this year.
"We were a long way off the pace. Unless we focus on it, we will sleep walk our way into the next one," Strauss told BBC Test Match Special.
"If we have a core of specialists we can prioritise both teams."
Test skipper Alastair Cook was removed as one-day captain and replaced by Eoin Morgan less than two months before the World Cup started in February.
England won only two of their six group games, against minnows Scotland and Afghanistan.
Former England captain Strauss said: "Our country is generally is quite red-ball focussed, but that doesn't mean it has to be at the expense of white-ball cricket.
"That's one of my focuses - to re-balance it and give more importance to it."
Only four England players involved in the current one-day series against Pakistan featured in the recent 2-0 Test series defeat.
Strauss said one-day specialists would have "opportunities" to compete in the lucrative Indian Premier League (IPL), which clashes with the start of the English season in April and May.
Asked about the IPL and the Big Bash, Australia's Twenty20 tournament, Strauss said: "I'm a massive fan.
"If you are an overseas player, what those Twenty20 competitions do is put you under real pressure.
"You have to stand up and deliver and that's a really good experience."
Manager Russell Slade says Cardiff must be more ruthless after they threw away a two-goal lead to draw with Burnley.
[NEXT_CONCEPT]
England director of cricket Andrew Strauss says "more separation" of the Test and one-day teams will improve their chances of winning the World Cup.