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."
Manager Russell Slade says Cardiff must be more ruthless after they threw away a two-goal lead to draw with Burnley.